Shellability of Kohnert posets
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911855092432896 |
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| author | Kerr, Celia Mayers, Nicholas W. Russoniello, Nicholas |
| author_facet | Kerr, Celia Mayers, Nicholas W. Russoniello, Nicholas |
| contents | In this paper, we are concerned with identifying among the family of posets associated with Kohnert polynomials, those whose order complex has a certain combinatorial property. In particular, for numerous families of Kohnert polynomials, including key polynomials, we determine when the associated Kohnert posets are (EL-)shellable. Interestingly, under certain diagram restrictions, (EL-)shellability of a Kohnert poset is equivalent to multiplcity freeness of the associated Kohnert polynomial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_17432 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Shellability of Kohnert posets Kerr, Celia Mayers, Nicholas W. Russoniello, Nicholas Combinatorics In this paper, we are concerned with identifying among the family of posets associated with Kohnert polynomials, those whose order complex has a certain combinatorial property. In particular, for numerous families of Kohnert polynomials, including key polynomials, we determine when the associated Kohnert posets are (EL-)shellable. Interestingly, under certain diagram restrictions, (EL-)shellability of a Kohnert poset is equivalent to multiplcity freeness of the associated Kohnert polynomial. |
| title | Shellability of Kohnert posets |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2404.17432 |