Combinatorial constructions of generating functions of cylindric partitions with small profiles into unrestricted or distinct parts

TL;DR

This paper develops combinatorial methods to construct generating functions for cylindric partitions with specific small profiles, linking them to ordinary partitions and covering both unrestricted and distinct parts cases.

Contribution

It introduces new combinatorial constructions for generating functions of cylindric partitions with small profiles, connecting them to classical partition theory.

Findings

Constructed generating functions for cylindric partitions with profiles (1,1) and (2,0)

Connected cylindric partitions to ordinary partitions through combinatorial methods

Covered both unrestricted and distinct parts cylindric partitions

Abstract

In this paper, cylindric partitions into profiles $c=(1,1)$ and $c=(2,0)$ are considered. The generating functions into unrestricted cylindric partitions and cylindric partitions into distinct parts with these profiles are constructed. The constructions are combinatorial and they connect the cylindric partitions with ordinary partitions.