New proofs of determinant evaluations related to plane partitions

TL;DR

This paper presents new proofs for determinant evaluations related to plane partitions, including a q-analogue, enhancing understanding and methods in enumerating symmetric plane partitions.

Contribution

The paper introduces novel proofs of Andrews's determinant and extends it with a q-analogue, providing new tools for enumerating plane partitions.

Findings

New proof of Andrews's determinant evaluation

Extension to a q-analogue of the determinant

Enhanced methods for counting symmetric plane partitions

Abstract

We give a new proof of a determinant evaluation due to Andrews, which has been used to enumerate cyclically symmetric and descending plane partitions. We also prove some related results, including a q-analogue of Andrews's determinant.