Equal values of certain partition functions via Diophantine equations

Abstract

Let $A\subset {\mathbb{N}}_{+}$ and by $P_A(n)$ denotes the number of partitions of an integer $n$ into parts from the set $A$. The aim of this paper is to prove several result concerning the existence of integer solutions of Diophantine equations of the form $P_A(x)=P_B(y)$, where $A,B$ are certain finite sets.

21 pages, submitted