Determinantal formulae for a symmetric generating function of totally symmetric plane partitions
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915983747186688 |
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| author | Hörmayer, Julia Schreier-Aigner, Florian |
| author_facet | Hörmayer, Julia Schreier-Aigner, Florian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_04626 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Determinantal formulae for a symmetric generating function of totally symmetric plane partitions Hörmayer, Julia Schreier-Aigner, Florian Combinatorics 05E05, 05A15, 05A19 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. |
| title | Determinantal formulae for a symmetric generating function of totally symmetric plane partitions |
| topic | Combinatorics 05E05, 05A15, 05A19 |
| url | https://arxiv.org/abs/2605.04626 |