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arXiv · 2610.04172

Unbounded log-concavity breaks in independence polynomials of spherically symmetric trees

César Bautista-Ramos
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Abstract

Using a dioid algebraic structure, we show that there exist spherically symmetric trees $T(2^m 1^n)$ whose independence polynomials exhibit multiple breaks in log-concavity, a result established by estimating the asymptotic growth of the coefficients of these polynomials. Provided the parameter $n$ is a sufficiently large odd integer, the number of breaks is bounded below by the Jacobsthal numbers. This result affirmatively answers a question raised by D. Galvin [D. Galvin, Trees with non log-concave independent set sequences, arXiv 2502.10654.v2].

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César Bautista-Ramos. 2026-10-03. Unbounded log-concavity breaks in independence polynomials of spherically symmetric trees. https://arxiv.org/abs/2610.04172

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