Asymptotics and congruences for partition functions which arise from finitary permutation groups

Finitary Permutation Groups

A finitary permutation group is a natural generalization of a finite permutation group. The structure of a transitive finitary permutation group is surprisingly simple when its degree is infinite. Here we study primitivity, following P. M. Neumann’s work in the 1970s. We also study generalized solubility conditions on these groups. These notes arose from lectures aimed at an audience who had se...

Asymptotics for Rank Partition Functions

In this paper, we obtain asymptotic formulas for an infinite class of rank generating functions. As an application, we solve a conjecture of Andrews and Lewis on inequalities between certain ranks.

On the Finitary Characterization of π-Congruences

Some alternative characterizations of late full congruences, either strong or weak, are presented. Those congruences are classically defined by requiring the corresponding ground bisimilarity under all name substitutions. We first improve on those infinitary definitions by showing that congruences can be alternatively characterized in the π-calculus by sticking to a finite number of carefully i...

Partition congruences by involutions

We present a general construction of involutions on integer partitions which enable us to prove a number of modulo 2 partition congruences. Introduction The theory of partitions is a beautiful subject introduced by Euler over 250 years ago and is still under intense development [2]. Arguably, a turning point in its history was the invention of the “constructive partition theory” symbolized by F...

Square - Partition Congruences