Results 151 to 160 of about 246,865 (191)
Optimal transport and integer partitions [PDF]
Discrete Applied Mathematics, 2015 : We link the theory of optimal transportation to the theory of integer partitions. Let P(n) denote the set of integer partitions of n is an element of N and write partitions pi is an element of P(n) as (n(1),..., n(k)(pi)).
Sonja Hohloch
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Bulletin of the Australian Mathematical Society, 2021
AbstractWe show that there are biases in the number of appearances of the parts in two residue classes in the set of ordinary partitions. More precisely, let $p_{j,k,m} (n)$ be the number of partitions of n such that there are more parts congruent to j modulo m than parts congruent to k modulo m for $m \geq 2$ . We prove that $p_{1,0,m} (n)$ is
BYUNGCHAN KIM, EUNMI KIM
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AbstractWe show that there are biases in the number of appearances of the parts in two residue classes in the set of ordinary partitions. More precisely, let $p_{j,k,m} (n)$ be the number of partitions of n such that there are more parts congruent to j modulo m than parts congruent to k modulo m for $m \geq 2$ . We prove that $p_{1,0,m} (n)$ is
BYUNGCHAN KIM, EUNMI KIM
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Stirling numbers and integer partitions
Quaestiones Mathematicae, 2016 In this paper, we prove that the Stirling numbers of both kinds can be written as sums over integer partitions. As corollaries, we rewrite some identities with Stirling numbers of both kinds without Stirling numbers.Keywords: Integer partitions ...
Mircea Merca
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On Product Partitions of Integers
Canadian Mathematical Bulletin, 1991AbstractLet p*(n) denote the number of product partitions, that is, the number of ways of expressing a natural number n > 1 as the product of positive integers ≥ 2, the order of the factors in the product being irrelevant, with p*(1) = 1. For any integer if d is an ith power, and = 1, otherwise, and let . Using a suitable generating function for p*(
Harris, V. C., Subbarao, M. V.
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On the Distribution of Multiplicities in Integer Partitions [PDF]
Annals of Combinatorics, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dimbinaina Ralaivaosaona
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Constrained Integer Partitions
2004We consider the problem of partitioning n integers into two subsets of given cardinalities such that the discrepancy, the absolute value of the difference of their sums, is minimized. The integers are i.i.d. random variables chosen uniformly from the set {1,...,M}. We study how the typical behavior of the optimal partition depends on n,M and the bias s,
Christian Borgs +3 more
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Integer partitions probability distributions [PDF]
Communications in Statistics - Theory and Methods, 2019 Two closely related discrete probability distributions are introduced. In each case the support is a set of vectors in $\mathbb{R}^n$ obtained from the partitions of the fixed positive integer $n$. These distributions arise naturally when considering equally-likely random permutations on the set of $n$ letters.
Andrew Sills
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The “best” partition of an integer
BIT, 1974An algorithm, based on a conjecture, to compute a permutation whose repeated application to a given set will yield a maximum number of different orderings of that set is presented. The algorithm gives the lengths of the cycles required. This problem turns out to be equivalent to the problem of determining a partitionB(n) ofn for which the least common ...
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On Intersecting Properties of Partitions of Integers
Combinatorics, Probability and Computing, 2005We derive a generalization of a theorem of Raimi proving there is a partition of natural numbers with given densities of classes which meet structured translates of any other class of a partition of natural numbers.
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2004
The theory of integer partitions is a subject of enduring interest. A major research area in its own right, it has found numerous applications, and celebrated results such as the Rogers-Ramanujan identities make it a topic filled with the true romance of mathematics.
George E. Andrews, Kimmo Eriksson
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The theory of integer partitions is a subject of enduring interest. A major research area in its own right, it has found numerous applications, and celebrated results such as the Rogers-Ramanujan identities make it a topic filled with the true romance of mathematics.
George E. Andrews, Kimmo Eriksson
openaire +1 more source