The Local $h$-Polynomials of Cluster Subdivisions Have Only Real Zeros

Philip B. Zhang

The Local $h$-Polynomials of Cluster Subdivisions Have Only Real Zeros

Combinatorics 2018-06-22 v2

Authors: Philip B. Zhang

Abstract

Athanasiadis raised the question whether the local $h$ -polynomials of type $A$ cluster subdivisions have only real zeros. In this paper, we confirm this conjecture and prove the real-rootedness of local $h$ -polynomials for all the other Cartan--Killing types. Our proofs mainly involve multiplier sequences and Chebyshev polynomials of the second kind.

Keywords

local h-polynomials cluster subdivisions real zeros real-rootedness Cartan–Killing types multiplier sequences Chebyshev polynomials of the second kind

Cite

@article{arxiv.1605.04780,
  title  = {The Local $h$-Polynomials of Cluster Subdivisions Have Only Real Zeros},
  author = {Philip B. Zhang},
  journal= {arXiv preprint arXiv:1605.04780},
  year   = {2018}
}

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9 pages

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