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Combinatorics and Statistical Mechanics of Integer Partitions [PDF]
Entropy, 2023 We study the set of integer partitions as a probability space that generates distributions and, in the asymptotic limit, obeys thermodynamics. We view ordered integer partition as a configuration of cluster masses and associate them with the distribution
Themis Matsoukas
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A central limit theorem for integer partitions into small powers. [PDF]
Mon Hefte Math, 2023 Lipnik GF, Madritsch MG, Tichy RF.
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Parting gravity’s tail: quadrupole tails at fifth order and beyond via integer partitions [PDF]
Journal of High Energy PhysicsThis work studies the systematic organization of higher-order gravitational quadrupole tails using generalized unitarity methods imported from the study of scattering amplitudes.
Alex Edison
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Partitions of an Integer into Powers [PDF]
Discrete Mathematics & Theoretical Computer Science, 2001 In this paper, we use a simple discrete dynamical model to study partitions of integers into powers of another integer. We extend and generalize some known results about their enumeration and counting, and we give new structural results.
Matthieu Latapy
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Some Special Integer Partitions Generated by a Family of Functions
Trends in Computational and Applied Mathematics, 2023 In this work, inspired by Ramanujan’s fifth order Mock Theta function f1(q), we define a collection 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
M. L. Matte
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Dynamics of the Picking transformation on integer partitions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2003 This paper studies a conservative transformation defined on families of finite sets. It consists in removing one element from each set and adding a new set composed of the removed elements.
Thi Ha Duong Phan, Eric Thierry
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$m$-noncrossing partitions and $m$-clusters [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 Let $W$ be a finite crystallographic reflection group, with root system $\Phi$. Associated to $W$ there is a positive integer, the generalized Catalan number, which counts the clusters in the associated cluster algebra, the noncrossing partitions for $W$,
Aslak Bakke Buan +2 more
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Additive Integer Partitions in R
Journal of Statistical Software, 2006 This paper introduces the partitions package of R routines, for numerical calculation of integer partititions. Functionality for unrestricted partitions, unequal partitions, and restricted partitions is provided in a small package that accompanies this ...
Robin K. S. Hankin
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On the Distribution of the spt-Crank
Mathematics, 2013 Andrews, Garvan and Liang introduced the spt-crank for vector partitions. We conjecture that for any n the sequence {NS (m, n)}m is unimodal, where NS (m, n) is the number of S-partitions of size n with crank m weight by the spt-crank.
Robert C. Rhoades +2 more
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ON SEQUENCES OF ELEMENTARY TRANSFORMATIONS IN THE INTEGER PARTITIONS LATTICE
Ural Mathematical Journal, 2023 An integer partition, or simply, a partition is a nonincreasing sequence \(\lambda = (\lambda_1, \lambda_2, \dots)\) of nonnegative integers that contains only a finite number of nonzero components. The length \(\ell(\lambda)\) of a partition \(\lambda\
Vitaly A. Baransky, Tatiana A. Senchonok
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