Log-concavity of inverse Kazhdan-Lusztig polynomials of paving matroids

Matthew H. Y. Xie; Philip B. Zhang

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arXiv · 2504.17567

Log-concavity of inverse Kazhdan-Lusztig polynomials of paving matroids

Matthew H. Y. Xie·Philip B. Zhang

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Abstract

Gao and Xie (2021) conjectured that the inverse Kazhdan-Lusztig polynomial of any matroid is log-concave. Although the inverse Kazhdan-Lusztig polynomial may not always have only real roots, we conjecture that the Hadamard product of an inverse Kazhdan-Lusztig polynomial of degree $n$ and $(1+t)^n$ has only real roots. Using interlacing polynomials and multiplier sequences, we confirm this conjecture for paving matroids. This result allows us to confirm the log-concavity conjecture for these matroids by applying Newton's inequalities.

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BibTeX RIS

Matthew H. Y. Xie, Philip B. Zhang. 2025-04-24. Log-concavity of inverse Kazhdan-Lusztig polynomials of paving matroids. https://arxiv.org/abs/2504.17567

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