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Relevant bibliographies by topics / Partities (Mathematics)

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Academic literature on the topic 'Partities (Mathematics)'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Partities (Mathematics)"

1

Moyer, Patricia Seray. "Links to Literature: A Remainder of One: Exploring Partitive Division." Teaching Children Mathematics 6, no. 8 (2000): 517–21. http://dx.doi.org/10.5951/tcm.6.8.0517.

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Children's literature can be a springboard for conversations about mathematical concepts. Austin (1998) suggests that good children's literature with a mathematical theme provides a context for both exploring and extending mathematics problems embedded in stories. In the context of discussing a story, children connect their everyday experiences with mathematics and have opportunities to make conjectures about quantities, equalities, or other mathematical ideas; negotiate their understanding of mathematical concepts; and verbalize their thinking. Children's books that prompt mathematical conver

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2

Andrews, George E., and Peter Paule. "MacMahon's partition analysis XII: Plane partitions." Journal of the London Mathematical Society 76, no. 3 (2007): 647–66. http://dx.doi.org/10.1112/jlms/jdm079.

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Hummel, Tamara Lakins. "Effective versions of Ramsey's Theorem: Avoiding the cone above 0′." Journal of Symbolic Logic 59, no. 4 (1994): 1301–25. http://dx.doi.org/10.2307/2275707.

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AbstractRamsey's Theorem states that if P is a partition of [ω]k into finitely many partition classes, then there exists an infinite set of natural numbers which is homogeneous for P. We consider the degrees of unsolvability and arithmetical definability properties of infinite homogeneous sets for recursive partitions. We give Jockusch's proof of Seetapun's recent theorem that for all recursive partitions of [ω]2 into finitely many pieces, there exists an infinite homogeneous set A such that ∅′ ≰TA. Two technical extensions of this result are given, establishing arithmetical bounds for such a

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HEDEN, OLOF. "A SURVEY OF THE DIFFERENT TYPES OF VECTOR SPACE PARTITIONS." Discrete Mathematics, Algorithms and Applications 04, no. 01 (2012): 1250001. http://dx.doi.org/10.1142/s1793830912500012.

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A vector space partition is here a collection [Formula: see text] of subspaces of a finite vector space V(n, q), of dimension n over a finite field with q elements, with the property that every non-zero vector is contained in a unique member of [Formula: see text]. Vector space partitions relate to finite projective planes, design theory and error correcting codes. In the first part of the paper I will discuss some relations between vector space partitions and other branches of mathematics. The other part of the paper contains a survey of known results on the type of a vector space partition,

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Caicedo, Andrés Eduardo, and Brittany Shelton. "Of Puzzles and Partitions: Introducing Partiti." Mathematics Magazine 91, no. 1 (2018): 20–23. http://dx.doi.org/10.1080/0025570x.2018.1403233.

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6

Andrews, George E., Peter Paule, and Axel Riese. "Macmahon's partition analysis IX: K-gon partitions." Bulletin of the Australian Mathematical Society 64, no. 2 (2001): 321–29. http://dx.doi.org/10.1017/s0004972700039988.

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Dedicated to George Szekeres on the occasion of his 90th birthdayMacMahon devoted a significant portion of Volume II of his famous book Combinatory Analysis to the introduction of Partition Analysis as a computational method for solving combinatorial problems in connection with systems of linear diophantine inequalities and equations. In a series of papers we have shown that MacMahon's method turns into an extremely powerful tool when implemented in computer algebra. In this note we explain how the use of the package Omega developed by the authors has led to a generalisation of a classical cou

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7

Józefiak, Tadeusz, and Jerzy Weyman. "Representation-theoretic interpretation of a formula of D. E. Littlewood." Mathematical Proceedings of the Cambridge Philosophical Society 103, no. 2 (1988): 193–96. http://dx.doi.org/10.1017/s0305004100064768.

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This note is a continuation of our attempts (see [3]) to give a satisfactory representation-theoretic justification of the following formula of D. E. Littlewood:where sI is the Schur symmetric function corresponding to a partition I, |I| is the weight of I, r(I) is the rank of I, and the summation ranges over all self-conjugate partitions (i.e. partitions I such that I = I where I is the partition conjugate to I).

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8

Goulden, I. P. "Exact Values for Degree Sums Over Strips of Young Diagrams." Canadian Journal of Mathematics 42, no. 5 (1990): 763–75. http://dx.doi.org/10.4153/cjm-1990-040-4.

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If λ = (λ1,…, λm) where λ1,…,λm are nonnegative integers with λ1 ≥…≥ λm, then λ is a partition of |λ| = λ1 + …+λm, and we write λ⊢ |λ|. The non-zero λi's are the parts of λ, so λ1 is the largest part, and ℓ(λ) is the number of parts of λ. Two partitions with the same parts, so they differ only in number of zeros, are the same. The set of all partitions, including the partition of 0 (with 0 parts) is denoted by The conjugate of λ, denoted by , is the partition (μ1,…, μk), in which μi is the number of λ's that are ≥i , for i = 1,…, k, where k=λ1.

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9

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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10

Bérard, P., and B. Helffer. "Remarks on the boundary set of spectral equipartitions." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 372, no. 2007 (2014): 20120492. http://dx.doi.org/10.1098/rsta.2012.0492.

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Given a bounded open set in (or in a Riemannian manifold), and a partition of Ω by k open sets ω j , we consider the quantity , where λ ( ω j ) is the ground state energy of the Dirichlet realization of the Laplacian in ω j . We denote by ℒ k ( Ω ) the infimum of over all k -partitions. A minimal k -partition is a partition that realizes the infimum. Although the analysis of minimal k -partitions is rather standard when k =2 (we find the nodal domains of a second eigenfunction), the analysis for higher values of k becomes non-trivial and quite interesting. Minimal partitions are in particular

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