Plane overpartitions and cylindric partitions

TL;DR

This paper explores generating functions for plane overpartitions, extends these to cylindric partitions, and establishes a correspondence between plane overpartitions and domino tilings, using combinatorial and algebraic methods.

Contribution

It introduces new generating functions for plane overpartitions and cylindric partitions, and links plane overpartitions to domino tilings, providing novel combinatorial insights.

Findings

Generated functions for plane overpartitions using multiple methods

Extended generating functions to cylindric partitions

Established correspondence between plane overpartitions and domino tilings

Abstract

Generating functions for plane overpartitions are obtained using various methods such as nonintersecting paths, RSK type algorithms and symmetric functions. We extend some of the generating functions to cylindric partitions. Also, we show that plane overpartitions correspond to certain domino tilings and we give some basic properties of this correspondence.