Strictly chained (p,q)-ary partitions

TL;DR

This paper studies a special class of integer partitions with parts of the form p^a q^b, where p and q are coprime, focusing on their generation, encoding, and asymptotic properties.

Contribution

It introduces a new class of partitions with divisibility restrictions and provides methods for generating and encoding them, along with estimates for related partition functions.

Findings

Developed algorithms for generating these partitions

Provided estimates for partition functions involving p and q

Analyzed the combinatorial structure of the partitions

Abstract

We consider a special type of integer partitions in which the parts of the form $p^aq^b$, for some relatively prime integers $p$ and $q$, are restricted by divisibility conditions. We investigate the problems of generating and encoding those partitions and give some estimates for several partition functions.