Bibliografías temáticas / Integer Partition Function

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Literatura académica sobre el tema "Integer Partition Function"

Autor: Grafiati
Publicado: 3 de junio de 2025
Última modificación: 31 de julio de 2025

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Artículos de revistas sobre el tema "Integer Partition Function"

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Davis, Simon. "A recursion relation for the number of Goldbach partitions of an even integer." Journal of Discrete Mathematical Sciences and Cryptography 27, no. 1 (2024): 1–30. http://dx.doi.org/10.47974/jdmsc-1188.

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The contour integral representation of the number of Goldbach partitions of an even integer, G(n), is extended to an integral with a support function that equals a linear combination of integers {G(m)}. A support function is found such that there is a nontrivial integral relation relating number of Goldbach partitions of n and m < n. The proof of the existence of a partition of any even integer greater than or equal to four into the sum of two primes follows from a recursion relation, resulting from an integral identity, that yields a non-zero lower bound for G(n). A partition of n, given a
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BERNDT, BRUCE C., AE JA YEE, and ALEXANDRU ZAHARESCU. "ON THE PARITY OF PARTITION FUNCTIONS." International Journal of Mathematics 14, no. 04 (2003): 437–59. http://dx.doi.org/10.1142/s0129167x03001740.

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Let S denote a subset of the positive integers, and let pS(n) be the associated partition function, that is, pS(n) denotes the number of partitions of the positive integer n into parts taken from S. Thus, if S is the set of positive integers, then pS(n) is the ordinary partition function p(n). In this paper, working in the ring of formal power series in one variable over the field of two elements Z/2Z, we develop new methods for deriving lower bounds for both the number of even values and the number of odd values taken by pS(n), for n ≤ N. New very general theorems are obtained, and applicatio
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Andrews, George. "Separable integer partition classes." Transactions of the American Mathematical Society, Series B 9, no. 21 (2022): 619–47. http://dx.doi.org/10.1090/btran/87.

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A classical method for partition generating function is developed into a tool with wide applications. New expansions of well-known theorems are derived, and new results for partitions with n n copies of n n are presented.
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GARVAN, FRANK G., and HAMZA YESILYURT. "SHIFTED AND SHIFTLESS PARTITION IDENTITIES II." International Journal of Number Theory 03, no. 01 (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 c
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Matte, M. L. "Some Special Integer Partitions Generated by a Family of Functions." Trends in Computational and Applied Mathematics 24, no. 4 (2023): 717–44. http://dx.doi.org/10.5540/tcam.2023.024.04.00717.

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In this work, inspired by Ramanujan’s fifth order Mock Theta function f1(q), we define acollection of functions and look at them as generating functions for partitions of some integer n containing at least m parts equal to each one of the numbers from 1 to its greatest part s, with no gaps.We set a two-line matrix representation for these partitions for any m ≥ 2 and collect the values of the sum of the entries in the second line of those matrices. These sums contain information about some parts of the partitions, which lead us to closed formulas for the number of partitions generated by our f
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Merca, Mircea. "Rank partition functions and truncated theta identities." Applicable Analysis and Discrete Mathematics, no. 00 (2021): 23. http://dx.doi.org/10.2298/aadm190401023m.

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In 1944, Freeman Dyson defined the concept of rank of an integer partition and introduced without definition the term of crank of an integer partition. A definition for the crank satisfying the properties hypothesized for it by Dyson was discovered in 1988 by G.E. Andrews and F.G. Garvan. In this paper, we introduce truncated forms for two theta identities involving the generating functions for partitions with non-negative rank and non-negative crank. As corollaries we derive new infinite families of linear inequalities for the partition function p(n). The number of Garden of Eden partitions a
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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 (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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Calkin, Neil, Jimena Davis, Kevin James, Elizabeth Perez, and Charles Swannack. "Computing the integer partition function." Mathematics of Computation 76, no. 259 (2007): 1619–39. http://dx.doi.org/10.1090/s0025-5718-07-01966-7.

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Kim, Jun Kyo, and Sang Guen Hahn. "Recursive formulae for the multiplicative partition function." International Journal of Mathematics and Mathematical Sciences 22, no. 1 (1999): 213–16. http://dx.doi.org/10.1155/s0161171299222132.

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For a positive integern, letf(n)be the number of essentially different ways of writingnas a product of factors greater than1, where two factorizations of a positive integer are said to be essentially the same if they differ only in the order of the factors. This paper gives a recursive formula for the multiplicative partition functionf(n).
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Hansen, Jennie C. "A functional central limit theorem for the Ewens sampling formula." Journal of Applied Probability 27, no. 1 (1990): 28–43. http://dx.doi.org/10.2307/3214593.

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For each n > 0, the Ewens sampling formula from population genetics is a measure on the set of all partitions of the integer n. To determine the limiting distributions for the part sizes of a partition with respect to the measures given by this formula, we associate to each partition a step function on [0, 1]. Each jump in the function equals the number of parts in the partition of a certain size. We normalize these functions and show that the induced measures on D[0, 1] converge to Wiener measure. This result complements Kingman's frequency limit theorem [10] for the Ewens partition struct
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Tesis sobre el tema "Integer Partition Function"

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Pétréolle, Mathias. "Quelques développements combinatoires autour des groupes de Coxeter et des partitions d'entiers." Thesis, Lyon 1, 2015. http://www.theses.fr/2015LYO10237/document.

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Cette thèse porte sur l'étude de la combinatoire énumérative, plus particulièrement autour des partitions d'entiers et des groupes de Coxeter. Dans une première partie, à l'instar de Han et de Nekrasov-Okounkov, nous étudions des développements combinatoires des puissances de la fonction êta de Dedekind, en termes de longueurs d'équerres de partitions d'entiers. Notre approche, bijective, utilise notamment les identités de Macdonald en types affines (en particulier le type C), généralisant l'approche de Han en type A. Nous étendons ensuite avec de nouveaux paramètres ces développements, grâce
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Lösch, Manfred. "Ungeordnete Zahlpartitionen mit k Parts, ihre 2^(k - 1) Typen und ihre typspezifischen erzeugenden Funktionen." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-95635.

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Jede ungeordnete Zahlpartition mit k Parts (k-Partiton) hat einen Typ, der mittels einer geordneten Partition von k definiert werden kann. Es können somit 2^(k - 1) Typen definiert werden. Pro Typ gibt es eine eindeutig nummerierbare erzeugende Funktion der geschlossenen Form. Mit Rekursionen können diese Funktionen in (unendlich lange) Potenzreihen expandiert werden. Mit diesen erzeugenden Funktionen lassen sich Bijektionen zwischen den Partitionsmengen verschiedener Typen aufspüren.
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Lösch, Manfred. "Ungeordnete Zahlpartitionen mit k Parts, ihre 2^(k - 1) Typen und ihre typspezifischen erzeugenden Funktionen." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-143512.

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Die 2^(k – 1) Typen der ungeordneten Zahlpartitionen mit k Parts (k-Partitionen) werden hier mit Hilfe der geordneten Partitionen von k definiert. Für jeden Typ gibt es eine erzeugende Funktion der geschlossenen Form mit eindeutiger Nummerierung. Die bekannte erzeugende Funktion der k-Partitionen ist die Summe dieser 2^(k – 1) typspezifischen erzeugenden Funktionen. Die Expansion dieser typspezifischen erzeugenden Funktionen in (unendlich lange) Potenzreihen ist rekursiv möglich. Untersucht werden Zerlegungen von erzeugenden Funktionen der einfachen Typen in erzeugende Funktionen anderer Typen
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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<br>Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica<br>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<br>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,
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Hančl, Jaroslav. "Obecná enumerace číselných rozkladů." Master's thesis, 2011. http://www.nusl.cz/ntk/nusl-300238.

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Název práce: Obecná enumerace číselných rozklad· Autor: Jaroslav Hančl Katedra: Katedra aplikované matematiky Vedoucí diplomové práce: doc. RNDr. Martin Klazar, Dr., KAM MFF UK Abstrakt: Předložená diplomová práce se zabývá asymptotikami počítacích funkcí ideál· číselných rozklad·. Jejím hlavním cílem je zjistit největší možný asympto- tický r·st počítací funkce rozkladového ideálu, která je nekonečněkrát rovna nule. Autor se na základě znalosti asymptotik vybraných rozkladových ideál· snaží po- mocí kombinatorických a základních analytických metod odvodit odhady hledané asymptotiky. Výsledkem
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Wu, Ya-Lan, and 吳雅蘭. "Computing Certain Generating Functions of Integer Partitions." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/58271156185735172301.

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碩士<br>國立彰化師範大學<br>數學系所<br>94<br>In this paper, we continue the work of Kuo-Jye Chen on applications of an identity of Abel to integer partitions. Our work leads to a new identity related to partition functions of Andrews and Stanley.
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Libros sobre el tema "Integer Partition Function"

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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. American Mathematical Society, 2014.

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Capítulos de libros sobre el tema "Integer Partition Function"

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Campbell, Geoffrey B. "Integer Partitions Generalized to Vector Partitions." In Vector Partitions, Visible Points and Ramanujan Functions. Chapman and Hall/CRC, 2024. http://dx.doi.org/10.1201/9781003174158-13.

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Barvinok, Alexander. "Partition Functions of Integer Flows." In Algorithms and Combinatorics. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-51829-9_8.

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Campbell, Geoffrey B. "Integer Partitions and Their Generating Functions." In Vector Partitions, Visible Points and Ramanujan Functions. Chapman and Hall/CRC, 2024. http://dx.doi.org/10.1201/9781003174158-3.

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Canfield, E. Rodney, and Herbert S. Wilf. "On the Growth of Restricted Integer Partition Functions." In Partitions, q-Series, and Modular Forms. Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4614-0028-8_4.

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Aguilar, Ricardo A., Louis Ehwerhemuepha, and Terence Sanger. "Investigating the Need for Personalized Assessment: An Example from Thyroid Function Tests." In Communications in Computer and Information Science. Springer Nature Switzerland, 2025. https://doi.org/10.1007/978-3-031-88346-0_5.

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Abstract Using population-wide thresholds assumes normal variation in thyroid hormone levels is the same across individuals which may leave patients (with varying medical histories) undiagnosed and untreated. This analysis aims to assess whether patient-specific thresholds for thyroid hormone laboratory tests are justifiable within a heterogeneous pediatric population. The study data, obtained from Cerner Real-World Data, consists of observations from January 2016 to December 2019 of pediatric patients with at least two laboratory records for thyrotropin (TSH), free thyroxine (T4), total T4, o
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Hoffman, P. N., and J. F. Humphreys. "Explicit Q-functions." In Projective Representations of the Symmetric Groups. Oxford University PressOxford, 1992. http://dx.doi.org/10.1093/oso/9780198535560.003.0009.

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Abstract More details concerning the Q-functions are given in this chapter. Motivated by Theorem 7.21, we first define a function Q a for each integer sequence α; but then immediately show that if α: is not a strict partition, then Q a is either zero or is a multiple of Q A for a certain γ in 𝒟. The Q a are needed in Chapter 10, but they also play a role in a Laurent identity, (9.5) here. This is a generating “expression” for the Q a. It could be re-interpreted as a raising operator formula, such as occurs in the theory of Schur functions, but we prefer to use the Laurent formulation. It leads
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"Generating functions." In Integer Partitions. Cambridge University Press, 2004. http://dx.doi.org/10.1017/cbo9781139167239.006.

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"Formulas for partition functions." In Integer Partitions. Cambridge University Press, 2004. http://dx.doi.org/10.1017/cbo9781139167239.007.

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Lang, Feng-Gong, and De-Bao Zhang. "On a New Kind of Quartic Integro-Spline Over a Uniform Partition." In Fuzzy Systems and Data Mining IX. IOS Press, 2023. http://dx.doi.org/10.3233/faia231093.

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In this paper, we construct a new kind of quartic integro-spline by applying two constraints on integral values to the piecewise polynomials on the first and the last subintervals, respectively. This quartic integro-spline does not require any additional given boundary values and is relatively simple to implement. It is theoretically proved that this integro-spline has a satisfactory convergence rate for approximating unknown functions and its derivatives at the knots. Especially for an unknown function y with fifth order derivative values of 0 at the left and right endpoints, its approximatio
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Hardy, G. H., and E. M. Wright. "The Representation Of A Number By Two Or Four Squares." In An Introduction To The Theory Of Numbers. Oxford University PressOxford, 2008. http://dx.doi.org/10.1093/oso/9780199219858.003.0020.

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Abstract Waring’s problem: the numbers g(k)and G(k). Waring’s problem is that of the representation of positive integers as sums of a fixed number sof non-negative kth powers. It is the particular case of the general problem of § 19.1 in which the aare and sis fixed. When k1, the problem is that of partitions into sparts of unrestricted form; such partitions are enumerated, as we saw in Ch. XIX, by the function it is plainly impossible to represent all integers if sis too small, for example if s= 1. Indeed it is impossible if s &amp;lt; k.
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Actas de conferencias sobre el tema "Integer Partition Function"

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Guerra, Victor S., and Gabriel L. Nazar. "A Partition-Aware VNF Placement Methodology for FPGA-Equipped NFVIs." In Simpósio Brasileiro de Redes de Computadores e Sistemas Distribuídos. Sociedade Brasileira de Computação, 2024. http://dx.doi.org/10.5753/sbrc.2024.1545.

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In the context of Network Function Virtualization (NFV), Field Programmable Gate Arrays (FPGAs) can be used to reduce bottlenecks introduced by the substitution of dedicated hardware middleboxes by virtualized implementations. The problem of placing Virtualized Network Functions (VNFs) on FPGA-equipped NFV infrastructures, however, imposes additional challenges that require an accurate modeling of the FPGA fabric. More specifically, simultaneous sharing of the FPGA requires careful partitioning of its resources into fixed regions that can be dynamically reconfigure and to which functions can b
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Kramm, Matthias. "Image Cluster Compression Using Partitioned Iterated Function Systems and Efficient Inter-image Similarity Features." In 2007 Third International IEEE Conference on Signal-Image Technologies and Internet-Based System SITIS. IEEE, 2007. http://dx.doi.org/10.1109/sitis.2007.144.

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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}. 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 acti
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Informes sobre el tema "Integer Partition Function"

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Kirchhoff, Helmut, and Ziv Reich. Protection of the photosynthetic apparatus during desiccation in resurrection plants. United States Department of Agriculture, 2014. http://dx.doi.org/10.32747/2014.7699861.bard.

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In this project, we studied the photosynthetic apparatus during dehydration and rehydration of the homoiochlorophyllous resurrection plant Craterostigmapumilum (retains most of the photosynthetic components during desiccation). Resurrection plants have the remarkable capability to withstand desiccation, being able to revive after prolonged severe water deficit in a few days upon rehydration. Homoiochlorophyllous resurrection plants are very efficient in protecting the photosynthetic machinery against damage by reactive oxygen production under drought. The main purpose of this BARD project was
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