Crystal skeleton polynomials with major index, charge and depth
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915658128687104 |
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| author | Kobayashi, Masato |
| author_facet | Kobayashi, Masato |
| contents | We introduce a new family of polynomials, crystal skeleton polynomials, to better understand enumeration of standard Young tableaux, quasi-Yamanouchi tableaux and interactions with Gessel's expansion of a Schur function, quasi-crystals and crystal skeletons as Maas-Gariépy introduced in 2023. After developing calculus of those polynomials, we organize thoughts on major index, charge, depth, inversions with RSK correspondence and a bivariate factorial. Also, we revisit the theorem on internal zeros of fake degree polynomials by Billey--Konvalinka--Swanson (2020). These results altogether improve Gessel's expansion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_06273 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Crystal skeleton polynomials with major index, charge and depth Kobayashi, Masato Combinatorics 2020 Primary:05E05, Secondary:05E10 We introduce a new family of polynomials, crystal skeleton polynomials, to better understand enumeration of standard Young tableaux, quasi-Yamanouchi tableaux and interactions with Gessel's expansion of a Schur function, quasi-crystals and crystal skeletons as Maas-Gariépy introduced in 2023. After developing calculus of those polynomials, we organize thoughts on major index, charge, depth, inversions with RSK correspondence and a bivariate factorial. Also, we revisit the theorem on internal zeros of fake degree polynomials by Billey--Konvalinka--Swanson (2020). These results altogether improve Gessel's expansion. |
| title | Crystal skeleton polynomials with major index, charge and depth |
| topic | Combinatorics 2020 Primary:05E05, Secondary:05E10 |
| url | https://arxiv.org/abs/2512.06273 |