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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.11979 |
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| _version_ | 1866910803815301120 |
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| author | Chapoton, Frédéric |
| author_facet | Chapoton, Frédéric |
| contents | We introduce a q-analogue of the classical Zeta polynomial of finite partially ordered sets, as a polynomial in one variable x with coefficients depending on the indeterminate q. We prove some properties of this polynomial invariant, including its behaviour with respect to duality, product and disjoint union. The leading term is a q-analogue of the number of maximal chains, but not always with non-negative coefficients. The value at q=0 turns out to be essentially the characteristic polynomial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_11979 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a q-analogue of the Zeta polynomial of posets Chapoton, Frédéric Combinatorics We introduce a q-analogue of the classical Zeta polynomial of finite partially ordered sets, as a polynomial in one variable x with coefficients depending on the indeterminate q. We prove some properties of this polynomial invariant, including its behaviour with respect to duality, product and disjoint union. The leading term is a q-analogue of the number of maximal chains, but not always with non-negative coefficients. The value at q=0 turns out to be essentially the characteristic polynomial. |
| title | On a q-analogue of the Zeta polynomial of posets |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2402.11979 |