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arXiv · 2605.04626

Determinantal formulae for a symmetric generating function of totally symmetric plane partitions

Julia Hörmayer·Florian Schreier-Aigner
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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.

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Julia Hörmayer, Florian Schreier-Aigner. 2026-05-06. Determinantal formulae for a symmetric generating function of totally symmetric plane partitions. https://arxiv.org/abs/2605.04626

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