Trees with non log-concave independent set sequences
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909999372959744 |
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| author | Galvin, David |
| author_facet | Galvin, David |
| contents | We construct a family of trees with independence numbers going to infinity for which the log-concavity relation for the independent set sequence of a tree $T$ in the family fails at around $α(T)\left(1-1/(16\log α(T))\right)$. Here $α(T)$ is the independence number of $T$. This resolves a conjecture of Kadrawi and Levit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_10654 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Trees with non log-concave independent set sequences Galvin, David Combinatorics 05C69 We construct a family of trees with independence numbers going to infinity for which the log-concavity relation for the independent set sequence of a tree $T$ in the family fails at around $α(T)\left(1-1/(16\log α(T))\right)$. Here $α(T)$ is the independence number of $T$. This resolves a conjecture of Kadrawi and Levit. |
| title | Trees with non log-concave independent set sequences |
| topic | Combinatorics 05C69 |
| url | https://arxiv.org/abs/2502.10654 |