Garsia--Remmel $q$-rook numbers are not always unimodal
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914335405637632 |
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| author | Lewis, Joel Brewster Morales, Alejandro H. |
| author_facet | Lewis, Joel Brewster Morales, Alejandro H. |
| contents | We show by an explicit example that the Garsia--Remmel $q$-rook numbers of Ferrers boards do not all have unimodal sequences of coefficients. This resolves in the negative a question from 1986 by the aforementioned authors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_19714 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Garsia--Remmel $q$-rook numbers are not always unimodal Lewis, Joel Brewster Morales, Alejandro H. Combinatorics 05A05, 05A30, 05A20, secondary 05E05, 05A17 We show by an explicit example that the Garsia--Remmel $q$-rook numbers of Ferrers boards do not all have unimodal sequences of coefficients. This resolves in the negative a question from 1986 by the aforementioned authors. |
| title | Garsia--Remmel $q$-rook numbers are not always unimodal |
| topic | Combinatorics 05A05, 05A30, 05A20, secondary 05E05, 05A17 |
| url | https://arxiv.org/abs/2410.19714 |