Determinantal formulae for a symmetric generating function of totally symmetric plane partitions
Combinatorics
2026-05-07 v1
Abstract
Ilse Fischer and the second author introduced in [Algebr. Comb. 7 (2024), no. 5, 1319-1345] a two parameter family of polynomials defined as sums over totally symmetric plane partitions and connected to alternating sign matrices and cyclically symmetric lozenge tilings of a hexagon with a triangular hole. In this paper we present several determinantal formulae leading to new lattice path models and a novel family of tableaux. The later illustrates that the polynomials of our interest can be thought of as generalisations of the three dual Littlewood identities.
Keywords
Cite
@article{arxiv.2605.04626,
title = {Determinantal formulae for a symmetric generating function of totally symmetric plane partitions},
author = {Julia Hörmayer and Florian Schreier-Aigner},
journal= {arXiv preprint arXiv:2605.04626},
year = {2026}
}