Relevant bibliographies by topics / Integer partition theory

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Integer partition theory'

Author: Grafiati
Published: 4 June 2021
Last updated: 10 February 2022

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Journal articles on the topic "Integer partition theory"

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GARVAN, FRANK G., and HAMZA YESILYURT. "SHIFTED AND SHIFTLESS PARTITION IDENTITIES II." International Journal of Number Theory 03, no. 01 (March 2007): 43–84. http://dx.doi.org/10.1142/s1793042107000808.

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Let S and T be sets of positive integers and let a be a fixed positive integer. An a-shifted partition identity has the form [Formula: see text] Here p(S,n) is the number partitions of n whose parts are elements of S. For all known nontrivial shifted partition identities, the sets S and T are unions of arithmetic progressions modulo M for some M. In 1987, Andrews found two 1-shifted examples (M = 32, 40) and asked whether there were any more. In 1989, Kalvade responded with a further six. In 2000, the first author found 59 new 1-shifted identities using a computer search and showed how these could be proved using the theory of modular functions. Modular transformation of certain shifted identities leads to shiftless partition identities. Again let a be a fixed positive integer, and S, T be distinct sets of positive integers. A shiftless partition identity has the form [Formula: see text] In this paper, we show, except in one case, how all known 1-shifted and shiftless identities follow from a four-parameter theta-function identity due to Jacobi. New shifted and shiftless partition identities are proved.
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Yan, Xiao-Hui. "Partitions of the set of nonnegative integers with identical representation functions." International Journal of Number Theory 15, no. 10 (November 2019): 1969–75. http://dx.doi.org/10.1142/s1793042119501070.

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Let [Formula: see text] be the set of nonnegative integers. For any set [Formula: see text], let [Formula: see text] denote the number of representations of [Formula: see text] as [Formula: see text] with [Formula: see text]. Chen and Wang proved that the set of positive integers can be partitioned into two subsets [Formula: see text] and [Formula: see text] such that [Formula: see text] for all [Formula: see text]. In this paper, we prove that, for a given integer [Formula: see text] and a partition [Formula: see text], there is an integer [Formula: see text] such that [Formula: see text] does not hold.
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RØDSETH, ØYSTEIN J., and JAMES A. SELLERS. "PARTITIONS WITH PARTS IN A FINITE SET." International Journal of Number Theory 02, no. 03 (September 2006): 455–68. http://dx.doi.org/10.1142/s1793042106000644.

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For a finite set A of positive integers, we study the partition function pA(n). This function enumerates the partitions of the positive integer n into parts in A. We give simple proofs of some known and unknown identities and congruences for pA(n). For n in a special residue class, pA(n) is a polynomial in n. We examine these polynomials for linear factors, and the results are applied to a restricted m-ary partition function. We extend the domain of pA and prove a reciprocity formula with supplement. In closing we consider an asymptotic formula for pA(n) and its refinement.
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Ballantine, Cristina, and Mircea Merca. "Combinatorial proof of the minimal excludant theorem." International Journal of Number Theory 17, no. 08 (February 26, 2021): 1765–79. http://dx.doi.org/10.1142/s1793042121500615.

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The minimal excludant of a partition [Formula: see text], [Formula: see text], is the smallest positive integer that is not a part of [Formula: see text]. For a positive integer [Formula: see text], [Formula: see text] denotes the sum of the minimal excludants of all partitions of [Formula: see text]. Recently, Andrews and Newman obtained a new combinatorial interpretation for [Formula: see text]. They showed, using generating functions, that [Formula: see text] equals the number of partitions of [Formula: see text] into distinct parts using two colors. In this paper, we provide a purely combinatorial proof of this result and new properties of the function [Formula: see text]. We generalize this combinatorial interpretation to [Formula: see text], the sum of least [Formula: see text]-gaps in all partitions of [Formula: see text]. The least [Formula: see text]-gap of a partition [Formula: see text] is the smallest positive integer that does not appear at least [Formula: see text] times as a part of [Formula: see text].
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BRENNAN, CHARLOTTE, ARNOLD KNOPFMACHER, and STEPHAN WAGNER. "The Distribution of Ascents of Size d or More in Partitions of n." Combinatorics, Probability and Computing 17, no. 4 (July 2008): 495–509. http://dx.doi.org/10.1017/s0963548308009073.

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A partition of a positive integer n is a finite sequence of positive integers a1, a2, . . ., ak such that a1+a2+ċ ċ ċ+ak=n and ai+1 ≥ ai for all i. Let d be a fixed positive integer. We say that we have an ascent of size d or more if ai+1 ≥ ai+d.We determine the mean, the variance and the limiting distribution of the number of ascents of size d or more (equivalently, the number of distinct part sizes of multiplicity d or more) in the partitions of n.
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Andrews, George E. "The Bhargava-Adiga Summation and Partitions." Journal of the Indian Mathematical Society 84, no. 3-4 (July 1, 2017): 151. http://dx.doi.org/10.18311/jims/2017/15836.

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The Bhargava-Adiga summation rivals the 1ψ1􀀀summation of Ramanujan in elegance. This paper is devoted to two applications in the theory of integer partitions leading to partition questions related to Gauss's celebrated three triangle theorem.
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Calkin, Neil, Jimena Davis, Kevin James, Elizabeth Perez, and Charles Swannack. "Computing the integer partition function." Mathematics of Computation 76, no. 259 (February 28, 2007): 1619–39. http://dx.doi.org/10.1090/s0025-5718-07-01966-7.

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KAAVYA, S. J. "CRANK 0 PARTITIONS AND THE PARITY OF THE PARTITION FUNCTION." International Journal of Number Theory 07, no. 03 (May 2011): 793–801. http://dx.doi.org/10.1142/s1793042111004381.

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A well-known problem regarding the integer partition function p(n) is the parity problem, how often is p(n) even or odd? Motivated by this problem, we obtain the following results: (1) A generating function for the number of crank 0 partitions of n. (2) An involution on the crank 0 partitions whose fixed points are called invariant partitions. We then derive a generating function for the number of invariant partitions. (3) A generating function for the number of self-conjugate rank 0 partitions.
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Svaiter, B. F., and N. F. Svaiter. "The distributional zeta-function in disordered field theory." International Journal of Modern Physics A 31, no. 25 (September 8, 2016): 1650144. http://dx.doi.org/10.1142/s0217751x1650144x.

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In this paper, we present a new mathematical rigorous technique for computing the average free energy of a disordered system with quenched randomness, using the replicas. The basic tool of this technique is a distributional zeta-function, a complex function whose derivative at the origin yields the average free energy of the system as the sum of two contributions: the first one is a series in which all the integer moments of the partition function of the model contribute; the second one, which cannot be written as a series of the integer moments, can be made as small as desired. This result supports the use of integer moments of the partition function, computed via replicas, for expressing the average free energy of the system. One advantage of the proposed formalism is that it does not require the understanding of the properties of the permutation group when the number of replicas goes to zero. Moreover, the symmetry is broken using the saddle-point equations of the model. As an application for the distributional zeta-function technique, we obtain the average free energy of the disordered [Formula: see text] model defined in a [Formula: see text]-dimensional Euclidean space.
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PENNISTON, DAVID. "ARITHMETIC OF ℓ-REGULAR PARTITION FUNCTIONS." International Journal of Number Theory 04, no. 02 (April 2008): 295–302. http://dx.doi.org/10.1142/s1793042108001341.

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Let bℓ(n) denote the number of ℓ-regular partitions of n, where ℓ is prime and 3 ≤ ℓ ≤ 23. In this paper we prove results on the distribution of bℓ(n) modulo m for any odd integer m > 1 with 3 ∤ m if ℓ ≠ 3.
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Dissertations / Theses on the topic "Integer partition theory"

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Konan, Isaac. "Rogers-Ramanujan type identities : bijective proofs and Lie-theoretic approach." Thesis, Université de Paris (2019-....), 2020. http://www.theses.fr/2020UNIP7087.

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Cette thèse relève de la théorie des partitions d’entiers, à l’intersection de la combinatoire et de la théorie de nombres. En particulier, nous étudions les identités de type Rogers-Ramanujan sous le spectre de la méthode des mots pondérés. Une révision de cette méthode nous permet d’introduire de nouveaux objets combinatoires au delà de la notion classique de partitions d’entiers: partitions colorées généralisées. À l’aide de ces nouveaux éléments, nous établissons de nouvelles identités de type Rogers-Ramanujanvia deux approches différentes. La première approche consiste en une preuve combinatoire, essentiellement bijective, des identités étudiées. Cette approche nous a ainsi permis d’établir des identités généralisant plusieurs identités importantes de la théorie: l’identité de Schur et l’identité Göllnitz, l’identité de Glaisher généralisant l’identité d’Euler, les identités de Siladić, de Primc et de Capparelli issues de la théorie des représentations de algèbres de Lie affines. La deuxième approche fait appel à la théorie des cristaux parfaits, issue de la théorie des représentations des algèbres de Lie affines. Nous interprétons ainsi le caractère des représentations standards comme des identités de partitions d’entiers colorées généralisées. En particulier, cette approche permet d’établir des formules assez simplifiées du caractère pour toutes les représentations standards de niveau 1 des types affines A(1) n-1, A(2) 2n , D(2) n+1, A(2) 2n-1, B(1) n , D(1) n
The topic of this thesis belongs to the theory of integer partitions, at the intersection of combinatorics and number theory. In particular, we study Rogers-Ramanujan type identities in the framework of the method of weighted words. This method revisited allows us to introduce new combinatorial objects beyond the classical notion of integer partitions: the generalized colored partitions. Using these combinatorial objects, we establish new Rogers-Ramanujan identities via two different approaches.The first approach consists of a combinatorial proof, essentially bijective, of the studied identities. This approach allowed us to establish some identities generalizing many important identities of the theory of integer partitions : Schur’s identity and Göllnitz’ identity, Glaisher’s identity generalizing Euler’s identity, the identities of Siladić, of Primc and of Capparelli coming from the representation theory of affine Lie algebras. The second approach uses the theory of perfect crystals, coming from the representation theory of affine Lie algebras. We view the characters of standard representations as some identities on the generalized colored partitions. In particular, this approach allows us to establish simple formulas for the characters of all the level one standard representations of type A(1) n-1, A(2) 2n , D(2) n+1, A(2) 2n-1, B(1) n , D(1) n
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Chen, Xujin, and 陳旭瑾. "Graph partitions and integer flows." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2004. http://hub.hku.hk/bib/B30286256.

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French, Jennifer. "Vector Partitions." Digital Commons @ East Tennessee State University, 2018. https://dc.etsu.edu/etd/3392.

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Integer partitions have been studied by many mathematicians over hundreds of years. Many identities exist between integer partitions, such as Euler’s discovery that every number has the same amount of partitions into distinct parts as into odd parts. These identities can be proven using methods such as conjugation or generating functions. Over the years, mathematicians have worked to expand partition identities to vectors. In 1963, M. S. Cheema proved that every vector has the same number of partitions into distinct vectors as into vectors with at least one component odd. This parallels Euler’s result for integer partitions. The primary purpose of this paper is to use generating functions to prove other vector partition identities that parallel results of integer partitions.
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Silva, Eduardo Alves da. "Formas ponderadas do Teorema de Euler e partições com raiz : estabelecendo um tratamento combinatório para certas identidades de Ramanujan." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2018. http://hdl.handle.net/10183/183163.

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O artigo Weighted forms of Euler's theorem de William Y.C. Chen e Kathy Q. Ji, em resposta ao questionamento de George E. Andrews, matemático estadunidense, sobre encontrar demonstrações combinatórias de duas identidades no Caderno Perdido de Ramanujan, nos mostra algumas formas ponderadas do Teorema de Euler sobre partições com partes ímpares e partes distintas via a introdução do conceito de partição com raiz. A propositura deste trabalho é envolta à apresentação de resultados sobre partições com raiz de modo a posteriormente realizar formulações combinatórias das identidades de Ramanujan por meio deste conceito, procurando estabelecer conexões com formas ponderadas do Teorema de Euler. Em particular, a bijeção de Sylvester e a iteração de Pak da função de Dyson são elementos primordiais para obtê-las.
The article Weighted forms of Euler's theorem by William Y.C. Chen and Kathy Q. Ji in response to the questioning of George E. Andrews, American mathematician, about nding combinatorial proofs for two identities in Ramanujan's Lost Notebook shows us some weighted forms of Euler's Theorem on partitions with odd parts and distinct parts through the introduction of the concept of rooted partition. The purpose of this work involves the presentation of results on rooted partitions in order to make combinatorial formulations of Ramanujan's identities, seeking to establish connections with weighted forms of Euler's Theorem. In particular, the Sylvester's bijection and the Pak's iteration of the Dyson's map are primordial elements to obtain them.
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Mucelin, Cláudio. "Demonstrações bijetivas em partições." [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306031.

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Orientador: Andréia Cristina Ribeiro
Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica
Made available in DSpace on 2018-08-17T16:44:00Z (GMT). No. of bitstreams: 1 Mucelin_Claudio_M.pdf: 744549 bytes, checksum: 062211ac0a3abf9bcf171fe9881dcafa (MD5) Previous issue date: 2011
Resumo: Este trabalho apresenta alguns resultados sobre partições de números inteiros e a importância deles na história da Matemática e da Teoria dos Números. Encontrar demonstrações bijetivas em partições não é nada fácil. Mas, depois de encontradas, tornam-se uma maneira agradável e fácil de entender e provar algumas Identidades de Partições. Este trabalho pretende ser didático e de fácil entendimento para futuras pesquisas de estudantes que se interessem pelo assunto. Ele traz definições básicas e importantes sobre partições, os Gráficos de Ferrers, demonstrações de resultados interessantes como a Bijeção de Bressoud e o Teorema Pentagonal de Euler. Destaca também a importância das funções geradoras e alguns resultados devidos a Sylvester, Dyson, Fine, Schur e Rogers-Ramanujan
Abstract: This work presents some results about partitions of integers numbers and their importance in the history of Mathematics and in the Theory of the Numbers. To find bijective demonstrations in partitions it is not easy. But, after finding them, to understand and to prove some Identities of Partitions becomes agreeable and easy. This work intends to be didatic and of easy understanding for future researches made by students interested in this subject. It contains basic and important definitions about partitions, the Ferrers' Graphics, demonstrations of interesting results as the Bressond's Bijection and the Euler's Pentagonal Theorem. It also details the importance of the generating functions and some results due to Sylvester, Dyson, Fine, Schur and Rogers-Ramanujan
Mestrado
Teoria dos Numeros
Mestre em Matemática
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Zini, Roger. "Placement, routage conjoints et hierarchiques de reseaux prediffuses." Paris 6, 1987. http://www.theses.fr/1987PA066116.

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Cette these propose un algorithme original de construction hierarchique d'arbres de steiner ainsi qu'une technique d'estimation de longueur au fur et a mesure de cette construction. Deux algorithmes de partitionnement d'hypergraphes, de maniere gloutonne ou par recuit simule sans rejets, y sont exposes. Elle introduit enfin un concept de directions d'attraction permettant d'effectuer un placement routage de circuits vlsi, a implanter sur des reseaux prediffuses, sous forme de systeme regule par retroaction entre le placement, le routage et l'analyse temporelle, afin d'obtenir du circuit, par un placement-routage adequat, les performances temporelles souhaitees
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Books on the topic "Integer partition theory"

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Alladi, Krishnaswami, Frank Garvan, and Ae Ja Yee. Ramanujan 125: International conference to commemorate the 125th anniversary of Ramanujan's birth, Ramanujan 125, November 5--7, 2012, University of Florida, Gainesville, Florida. Providence, Rhode Island: American Mathematical Society, 2014.

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Book chapters on the topic "Integer partition theory"

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Sane, Sharad S. "Partition theory of integers." In Texts and Readings in Mathematics, 325–52. Gurgaon: Hindustan Book Agency, 2013. http://dx.doi.org/10.1007/978-93-86279-55-2_13.

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Sebő, András. "Path Partitions, Cycle Covers and Integer Decomposition." In Graph Theory, Computational Intelligence and Thought, 183–99. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-02029-2_18.

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Schwartz, Richard Evan. "The Plaid Master Picture Theorem." In The Plaid Model, 93–102. Princeton University Press, 2019. http://dx.doi.org/10.23943/princeton/9780691181387.003.0009.

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This chapter aims to prove Theorem 1.4 and Theorem 0.3, the Plaid Master Picture Theorem. Both of these results are deduced from Theorem 8.2, which says that the union PLA of plaid polygons is generated by an explicitly defined tiling classifying space (ලA, XP). Moreover, there is a nice space X which has the individual spaces XP as rational slices. The space X has a partition into convex polytopes, and one obtains the partition of XP by intersecting the relevant slice with this partition. Section 8.2 describes the space X. Section 8.3 describes the partition of X into convex integer polytopes. The partition is called the checkerboard partition. Section 8.4 explains the classifying map Φ‎A : Π‎ → XP. Section 8.5 states Theorem 8.2 and deduces Theorem 1.4 and Theorem 0.3 from it.
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Schwartz, Richard Evan. "Proof of the Main Result." In The Plaid Model, 125–32. Princeton University Press, 2019. http://dx.doi.org/10.23943/princeton/9780691181387.003.0013.

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This chapter puts together the ingredients from the last three chapters—the Segment Lemma, the Horizontal Lemma, and the Vertical Lemma—and proves Theorem 8.2. The three technical lemmas do not mention the partition of the space X at all, but they do give a lot of control over how the nature of the particles tracked by points in the plaid grid Π‎ influences the image of such grid points under the classifying map Φ‎. What remains is to compare the three results above to the partition and determine whether everything matches. The remainder of the chapter is organized as follows. Section 12.2 carries out the program to show that these containers are each a union of two prisms. Section 12.3 discusses some extra symmetry of the partition. Section 12.5 compares the prism containers in the vertical case to the partition of X and deduces that Theorem 8.2 is true for the vertical unit integer segments. Section 12.4 compares the prism containers in the vertical case to the partition of X and deduces that Theorem 8.2 is true for the horizontal unit integer segments. The two results together complete the proof.
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Schwartz, Richard Evan. "The Orbit Equivalence Theorem." In The Plaid Model, 173–84. Princeton University Press, 2019. http://dx.doi.org/10.23943/princeton/9780691181387.003.0018.

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This chapter begins Part 4 of the monograph. The goal of this part is to prove the Orbit Equivalence Theorem and the Quasi-Isomorphism Theorem. Theorem 17.1 (Orbit Equivalence) states that there is a dynamically large subset Z ⊂ X and a map Ω‎: Z → Y. Section 17.2 defines Z. Section 17.3 defines Ω‎. Section 17.4 characterizes the image Ω‎(Z). Section 17.5 defines a partition of Z into small convex polytopes which have the property that all the maps in Equations 17.1 and 1 are entirely defined and projective on each polytope. This allows us to verify the properties in the Orbit Equivalence Theorem just by checking what the two relevant maps do to the vertices of the new partition. Section 17.6 puts everything together and prove the Orbit Equivalence Theorem modulo some integer computer calculations. Section 17.7 discusses the computational techniques used to carry out the calculations from Section 17.6. Section 17.8 explains the calculations.
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"On Partitions of the Positive Integers With No x, y, z Belonging to Distinct Classes Satisfying x + y = z." In Number Theory, 515–28. De Gruyter, 1990. http://dx.doi.org/10.1515/9783110848632-042.

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Lobna, Kallel, Kamoun Hichem, and Benaissa Mounir. "A Multi-Objective Model for the Simultaneous Planning Problems." In Transportation, Logistics, and Supply Chain Management in Home Healthcare, 111–35. IGI Global, 2020. http://dx.doi.org/10.4018/978-1-7998-0268-6.ch007.

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This chapter examines two of the most important operational problems in seaport terminals, first, the berth allocation problem (BAP) which finds an optimal assignment of ships to the berths that minimise the total waiting time of all ships. Then we consider the ships containers to storage areas assignment problem (SSAP) which finds an allocation of ship containers to storage area that minimises the travelling time and containers dispersion. In the first step, a mixed integer linear program model is designed to address the BA problem with the aim of minimising the ships stay time in the port (known as the scheduling theory by the flow time). In a second step, the output of the first model is used in another mixed integer linear program model to solve the SSA problem with a view at reducing both travelling time and containers dispersion while satisfying storage capacities for the case where the containers of one ship can be partitioned into two different and consecutive storage area when needed. The experimental part is conducted on a real case, namely the Tunisian port of Radès.
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"Hierarchical Order II." In Boundedness and Self-Organized Semantics: Theory and Applications, 70–87. IGI Global, 2013. http://dx.doi.org/10.4018/978-1-4666-2202-9.ch004.

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The self-organization under boundedness is considered as an operational protocol, which describes the highly non-trivial interplay between the inter-level feedback and the spatio-temporal pattern that describes the corresponding homeostasis. A generic property of the feedback is that it sets metrics in the state space and defines the admissible transitions from any given state. Further, the state space is partitioned into basins-of-attraction so that each of them is tangent to the point called accumulation point. A distinctive property of the basins-of-attraction is that the discrete band of the power spectrum appears as intra-basin invariant and thus turns as appropriate candidate for a “letter.” The accumulation point is associated with the notion of a “space bar.” Then, since the motion in a bounded attractor is orbital, it is appropriate to associate a “word” with an orbit. The latter open the door for assigning a specific non-mechanical engine to each and every orbit. In turn the functional irreversibility of any engine substantiates the sensitivity to permutations of every semantic unit.
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Mertens, Stephan. "The Easiest Hard Problem: Number Partitioning." In Computational Complexity and Statistical Physics. Oxford University Press, 2005. http://dx.doi.org/10.1093/oso/9780195177374.003.0012.

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The number partitioning problem (NPP) is defined easily: Given a list a1, a2, . . . , an of positive integers, find a partition, that is, a subset A {1,..., n}, minimizing the discrepancy Number partitioning is of considerable importance, both practically and theoretically. Its practical applications range from multiprocessor scheduling and the minimization of VLSI circuit size and delay [102, 504], to public key cryptography [387], to choosing up sides in a ball game [237]. Number partitioning is also one of Garey and Johnson's six basic NP-hard problems that lie at the heart of the theory of NP-completeness [191, 388], and is in fact the only one of these problems that actually deals with numbers. Hence, it is often chosen as a base for NP-completeness proofs of other problems involving numbers, such as bin packing, multiprocessor scheduling [38], quadratic programming, and knapsack problems. The computational complexity of the NPP depends on the type of input numbers {a1, a2 , . . . , an}. Consider the case where the values of aj are positive integers bounded by a constant A. Then the discrepancy E can take on at most nA different values, so the size of the search space is O(nA) instead of O(2n) and it is straightforward to devise an algorithm that explores this reduced space in time polynomial in nA [191]. Of course, such an algorithm does not prove P = NP: a concise encoding of an instance requires O(nlog2 A) bits, and A is not bounded by any power of Iog2 A. This feature of the NPP is called pseudopoly nomiality. The NP-hardness of the NPP becomes apparent when input numbers are of a size exponentially large in n or, after division by the maximal input number, of exponentially high precision. To study typical properties of the NPP, the input numbers are often taken to be independent, identically distributed random variables. Under this probabilistic assumption, the minimal discrepancy E0 is a stochastic quantity.
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Fleury, Martin, and Laith Al-Jobouri. "Data Partitioning." In Advances in Multimedia and Interactive Technologies, 118–58. IGI Global, 2016. http://dx.doi.org/10.4018/978-1-4666-8850-6.ch004.

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Data partitioning is a source-coding technique that has existed in one form or another in the standardized hybrid video codecs up to recent times. In essence, it is a method of prioritizing coding data, resulting in video layers that can be separately communicated across an error-prone network. The Chapter includes the background that has led to data partitioning being included in the standardized codecs. As this Chapter discusses, it differs from scalable video because the output from conventional, single-layer encoders can be converted to multi-layer form, rather than requiring specialist codec extensions. It is shown that the methods of forming the partitions so far employed are: dividing transformed, residual coefficients into two or more layers; and dividing coded data by function into headers, intra-, and inter-coded residuals to form three or more layers. It is also shown how layering naturally combines with protection by channel coding. Used as an error resilience tool, data partitioning presents a low overhead method, suitable for benign as well as bad channels. And in the three-layer variety, error concealment at the decoder can significantly aid the reconstruction of damaged video frames. The Chapter will be of particular interest to developers charged with making a mobile, low-latency, or interactive video streaming application robust, as they can select from the data-partitioning methods and apply them to open-source code of the recent High Efficiency Video Coding (HEVC) codec standard. Broadcast TV can also benefit from data partitioning. Developers of codecs additionally will find in this Chapter a guide to research and ideas about data partitioning which could be incorporated into future codecs.
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Conference papers on the topic "Integer partition theory"

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Chen, Pingen, and Qinghua Lin. "Simultaneous Optimization of Configuration and Control for a Passive SCR System." In ASME 2018 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/dscc2018-9243.

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The configuration and control of aftertreatment systems have a significant impact on their functionalities and emission control performance. The traditional aftertreatment system configurations, i.e., connections from one aftertreatment subsystem to another subsystem in series, are simple but generally do not yield the optimal aftertreatment system performance. New aftertreatment configurations, in conjunction with new engine and aftertreatment control, can significantly improve engine efficiency and emission reduction performance. However, new configuration design requires human intuition and in-depth knowledge of engine and aftertreatment system design and control. The purpose of this study is to develop a general systematic and computationally-efficient method which enables automated and simultaneous optimization of passive selective catalytic reduction (SCR) system architectures and the associated non-uniform cylinder-to-cylinder combustion (NUCCC) controls based on a newly proposed highly reconfigurable passive SCR model structure and integer partition theory. The proposed method is general enough to account for passive SCR systems with two or more TWC stages. We demonstrate through this case study that the optimized passive SCR configuration, in conjunction with the optimized NUCCC control, can reduce the NH3 specific fuel consumption by up to 21.90%.
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2

Krishnamachari, Ramprasad S., and Panos Y. Papalambros. "Optimal Hierarchical Decomposition Synthesis Using Integer Programming." In ASME 1996 Design Engineering Technical Conferences and Computers in Engineering Conference. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/96-detc/dac-1088.

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Abstract Decomposition synthesis in optimal design is the process of creating an optimal design model by selecting objectives and constraints so that it can be directly partitioned into an appropriate decomposed form. Such synthesis results are not unique since there may be many partitions that satisfy the decomposition requirements. Introducing suitable criteria an optimal decomposition synthesis process can be defined in a manner analogous to optimal partitioning formulations. The article presents an integer programming formulation and solution techniques for synthesizing hierarchically decomposed optimal design problems. Examples for designing a pressure vessel, an automotive caliper disc brake and a speed reducer are also presented.
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Vouillarmet, André, and Isabelle Trebinjac. "Improvements in L2F Anemometry Technique for Inter-Blade Investigations in High-Speed Turbomachinery." In ASME 1998 International Gas Turbine and Aeroengine Congress and Exhibition. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/98-gt-157.

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This paper presents some problems inherent in the application of a laser two-focus anemometry technique to measurement in high-speed small-scale compressors. Improvements in data processing are described, in relation to reducing the acquisition time. Measurement uncertainties and their possible estimation are discussed. An optimized blade pitch partition during synchronized measurements within rotating blade passages is presented using a prediction of shadow zones. Two examples highlight the resulting benefits both in terms of reduction of the acquisition time and improvement of the azimuthal resolution.
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Pu, Fan. "Investigation of Subcooled Flow Boiling Model Under Low Pressure." In 18th International Conference on Nuclear Engineering. ASMEDC, 2010. http://dx.doi.org/10.1115/icone18-29200.

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Two fluid model integrating a set of closure relationships (such as inter-phase heat transfer model, inter-phase mass transfer model, inter-phase momentum transfer model, mean bubble diameter model, bubble departure diameter model, bubble departure frequency model, onset of nucleate boiling model, wall heat flux partition model) are applied to solve the local flow and heat transfer of subcooled flow boiling under low pressure, and local flow parameters such as volume fraction, liquid velocity, vapor phase etc. are obtained using developed code. The subcooled flow boiling results predicted in this paper are compared to the subcooled flow boiling experimental results of TH Lee etc. in annular channel with inner tube heated uniformly and adiabatic outer tube, and they agree well. The code can also be used to predict the multiphase flow field in power reactor core when the subcooled flow boiling take place and the critical heat flux of Departure Nucleate Boiling (DNB) in reactor core and it is meaningful for reactor core design.
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Marchesi, Alberto, Matteo Castiglioni, and Nicola Gatti. "Leadership in Congestion Games: Multiple User Classes and Non-Singleton Actions." In Twenty-Eighth International Joint Conference on Artificial Intelligence {IJCAI-19}. California: International Joint Conferences on Artificial Intelligence Organization, 2019. http://dx.doi.org/10.24963/ijcai.2019/69.

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We study the problem of finding Stackelberg equilibria in games with a massive number of players. So far, the only known game instances in which the problem is solved in polynomial time are some particular congestion games. However, a complete characterization of hard and easy instances is still lacking. In this paper, we extend the state of the art along two main directions. First, we focus on games where players' actions are made of multiple resources, and we prove that the problem is NP-hard and not in Poly-APX unless P = NP, even in the basic case in which players are symmetric, their actions are made of only two resources, and the cost functions are monotonic. Second, we focus on games with singleton actions where the players are partitioned into classes, depending on which actions they have available. In this case, we provide a dynamic programming algorithm that finds an equilibrium in polynomial time, when the number of classes is fixed and the leader plays pure strategies. Moreover, we prove that, if we allow for leader's mixed strategies, then the problem becomes NP-hard even with only four classes and monotonic costs. Finally, for both settings, we provide mixed-integer linear programming formulations, and we experimentally evaluate their scalability on both random game instances and worst-case instances based on our hardness reductions.
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