Results 41 to 50 of about 863,417 (323)
Boltzmann Complexity: An Emergent Property of the Majorization Partial Order
Entropy, 2016 Boltzmann macrostates, which are in 1:1 correspondence with the partitions of integers, are investigated. Integer partitions, unlike entropy, uniquely characterize Boltzmann states, but their use has been limited.
William Seitz, A. D. Kirwan
doaj +1 more source
A PROOF OF ANDREWS’ CONJECTURE ON PARTITIONS WITH NO SHORT SEQUENCES
Forum of Mathematics, Sigma, 2019 Our main result establishes Andrews’ conjecture for the asymptotic of the generating function for the number of integer partitions of $n$ without $k$ consecutive parts.
DANIEL M. KANE, ROBERT C. RHOADES
doaj +1 more source
The number of parts in certain residue classes of integer partitions [PDF]
, 2015 We use the Circle Method to derive asymptotics for functions related to the number of parts of partitions in particular residue classes.
Olivia Beckwith, Michael H. Mertens
semanticscholar +1 more source
A phase transition in the distribution of the length of integer partitions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We assign a uniform probability to the set consisting of partitions of a positive integer $n$ such that the multiplicity of each summand is less than a given number $d$ and we study the limiting distribution of the number of summands in a random ...
Dimbinaina Ralaivaosaona
doaj +1 more source
A Nekrasov-Okounkov type formula for affine $\widetilde{C}$ [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 In 2008, Han rediscovered an expansion of powers of Dedekind $\eta$ function due to Nekrasov and Okounkov by using Macdonald's identity in type $\widetilde{A}$.
Mathias Pétréolle
doaj +1 more source
Composite Fermions and Integer Partitions
Journal of Combinatorial Theory, Series A, 2001 The authors prove the unimodality of integer partitions with at most \(a\) parts, all parts less than or equal to \(b\), that are required to contain either repeated or consecutive parts. The proof uses the KOH theorem [\textit{D. Zeilberger}, Am. Math. Mon. 96, No. 7, 590-602 (1989; Zbl 0726.05005)].
Arthur T. Benjamin +3 more
openaire +2 more sources
Hardware acceleration of number theoretic transform for zk‐SNARK
Engineering Reports, EarlyView., 2023 An FPGA‐based hardware accelerator with a multi‐level pipeline is designed to support the large‐bitwidth and large‐scale NTT tasks in zk‐SNARK. It can be flexibly scaled to different scales of FPGAs and has been equipped in the heterogeneous acceleration system with the help of HLS and OpenCL.
Haixu Zhao +6 more
wiley +1 more source
Unified derivation of the limit shape for multiplicative ensembles of random integer partitions with equiweighted parts [PDF]
Random Struct. Algorithms, 2011 We derive the limit shape of Young diagrams, associated with growing integer partitions, with respect to multiplicative probability measures underpinned by the generating functions of the form ℱ(z)=∏ℓ=1∞ℱ0(zℓ) (which entails equal weighting among ...
L. Bogachev
semanticscholar +1 more source
Numerical Estimation of the Asymptotic Behaviour of Solid Partitions of an Integer
, 2003 The number of solid partitions of a positive integer is an unsolved problem in combinatorial number theory. In this paper, solid partitions are studied numerically by the method of exact enumeration for integers up to 50 and by Monte Carlo simulations ...
Andrews G E +21 more
core +1 more source
The lattice of integer partitions
Discrete Mathematics, 1973 AbstractIn this paper we study the lattice Ln of partitions of an integer n ordered by dominance. We show Ln to be isomorphic to an infimum subsemilattice under the component ordering of certain concave nondecreasing (n+1)-tuples. For Ln, we give the covering relation, maximal covering number, minimal chains, infimum and supremum irreducibles, a chain ...
openaire +3 more sources