A note on the log-concavity of parking functions
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866912170543939584 |
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| author | Pappe, Joseph |
| author_facet | Pappe, Joseph |
| contents | We settle a conjecture of Bóna regarding the log-concavity of a certain statistic on parking functions by utilizing recent log-concavity results on matroids. This result allows us to also prove that connected, labeled graphs graded by their number of edges are log-concave. Furthermore, we generalize these results to $G$-parking functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_19783 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on the log-concavity of parking functions Pappe, Joseph Combinatorics Primary: 05A15, 05C30, Secondary: 05C05, 05C31 We settle a conjecture of Bóna regarding the log-concavity of a certain statistic on parking functions by utilizing recent log-concavity results on matroids. This result allows us to also prove that connected, labeled graphs graded by their number of edges are log-concave. Furthermore, we generalize these results to $G$-parking functions. |
| title | A note on the log-concavity of parking functions |
| topic | Combinatorics Primary: 05A15, 05C30, Secondary: 05C05, 05C31 |
| url | https://arxiv.org/abs/2412.19783 |