Strict unimodality of q-polynomials of rooted trees

Abstract

We classify rooted trees which have strictly unimodal q-polynomials (plucking polynomial). We also give criteria for a trapezoidal shape of a plucking polynomial. We generalize results of Pak and Panova on strict unimodality of q-binomial coefficients. We discuss which polynomials can be realized as plucking polynomials and whether or not different rooted trees can have the same plucking polynomial.

26 pages, 14 figures

References in corpus (3)

• Strict unimodality of q-binomial coefficients
• A combinatorial proof of strict unimodality for $q$-binomial coefficients
• Progress in distributive homology: from q-polynomial of rooted trees to Yang-Baxter homology

Cited by in corpus (3)

• Expansion Posets for Polygon Cluster Algebras
• Search for torsion in Khovanov homology
• Rooted trees with the same plucking polynomial