Results 31 to 40 of about 863,417 (323)
$m$-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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Alignment of rods and partition of integers [PDF]
Physical Review E, 2006 We study dynamical ordering of rods. In this process, rod alignment via pairwise interactions competes with diffusive wiggling. Under strong diffusion, the system is disordered, but at weak diffusion, the system is ordered. We present an exact steady-state solution for the nonlinear and nonlocal kinetic theory of this process.
Eli Ben-Naim, P. L. Krapivsky
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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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Multisectioned partitions of integers [PDF]
Pacific Journal of Mathematics, 1977 This paper presents identities on generating functions for multisectioned partitions of integers by developing in the language of partitions some powerful and essentially combinatorial techniques from the literature of principal differential ideals. D. Mead has stated in Vol. 42 of this journal that one can obtain interesting combinatorial relations by
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The topology of restricted partition posets [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 For each composition $\vec{c}$ we show that the order complex of the poset of pointed set partitions $Π ^• _{\vec{c}}$ is a wedge of $β\vec{c}$ spheres of the same dimensions, where $β\vec{c}$ is the number of permutations with descent composition ^$\vec{
Richard Ehrenborg, JiYoon Jung
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The Fractal and The Recurrence Equations Concerning The Integer Partitions
, 2020 This paper introduced a way of fractal to solve the problem of taking count of the integer partitions, furthermore, using the method in this paper some recurrence equations concerning the integer partitions can be deduced, including the pentagonal number
Zhang, Meng
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Statistical mechanics approach in the counting of integer partitions [PDF]
, 2016 The treatment of the number-theoretical problem of integer partitions within the approach of statistical mechanics is discussed. Historical overview is given and known asymptotic results for linear and plane partitions are reproduced.
Andrij Rovenchak
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Asymptotic prime partitions of integers [PDF]
Physical Review E, 2017 In this paper, we discuss P(n), the number of ways a given integer n may be written as a sum of primes. In particular, an asymptotic form P-as(n) valid for n ->infinity is obtained analytically using standard techniques of quantum statistical mechanics. First, the bosonic partition function of primes, or the generating function of unrestricted prime
Bartel, Johann +3 more
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