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Congruences for Andrews' spt-function modulo 32760 and extension of Atkin's Hecke-type partition congruences
Andrews' spt-function Atkin's Hecke-type partition congruences
2010/11/15
New congruences are found for Andrews' smallest parts partition function spt(n). The generating function for spt(n) is related to the holomorphic part alpha(24z) of a certain weak Maass form M(z) of ...
On the growth of restricted integer partition functions
integer partitions asymptotic growth
2010/12/10
We study the rate of growth of p(n, S,M), the number of partitions of n whose parts all belong to S and whose multiplicities all belong to M, where S (resp. M) are given infinite sets of positive (res...
Canonical and grand canonical partition functions of Dyson gases as tau-functions of integrable hierarchies and their fermionic realization
partition functions integrable hierarchies Dyson gases
2010/4/2
The partition function for a canonical ensemble of 2D Coulomb charges in a background potential (the Dyson gas) is realized as a vacuum expectation value of a group-like element constructed in terms o...
T=0 Partition Functions for Potts Antiferromagnets on Square Lattice Strips with (Twisted) Periodic Boundary Conditions
Functions Potts Antiferromagnets Periodic Boundary Conditions
2010/11/2
We present exact calculations of the zero-temperature partition function for the q-state Potts antiferromagnet (equivalently, the chromatic polynomial) for two families of arbitrarily long strip graph...
Exact Potts Model Partition Functions on Ladder Graphs
Exact Potts Model Partition Functions Ladder Graphs
2010/11/2
We present exact calculations of the partition function $Z$ of the $q$-state Potts model and its generalization to real $q$, the random cluster model, for arbitrary temperature on $n$-vertex ladder gr...