Trees with non log-concave independent set sequences

• DOI: 10.48550/arxiv.2502.10654
• Publication Date: 2025-01-01
• Authors: Galvin, David
• Keywords: 05C69; FOS: Mathematics; Mathematics - Combinatorics; Combinatorics (math.CO)

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.