The unimodality of the Ehrhart $\delta$-polynomial of the chain polytope of the zig-zag poset
| Autor: | Chen, Herman Z. Q., Zhang, Philip B. |
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| Rok vydání: | 2016 |
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| Druh dokumentu: | Working Paper |
| Popis: | We prove the unimodality of the Ehrhart $\delta$-polynomial of the chain polytope of the zig-zag poset, which was conjectured by Kirillov. First, based on a result due to Stanley, we show that this polynomial coincides with the $W$-polynomial for the zig-zag poset with some natural labeling. Then, its unimodality immediately follows from a result of Gasharov, which states that the $W$-polynomials of naturally labeled graded posets of rank $1$ or $2$ are unimodal. Comment: 6 pages |
| Databáze: | arXiv |
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