Séminaire Lotharingien de Combinatoire, 91B.64 (2024), 12 pp.

Petter Brändén and Leonardo Saud Maia Leite

Chain Polynomials of Generalized Paving Matroids

Abstract. We prove that the chain polynomial of the lattice of flats of a paving matroid is real-rooted, and we define a class of matroids called generalized paving matroids. Generalized paving matroids associated to subspace lattices are shown to have real-rooted chain polynomials, by a study of a q-analog of the subdivision operator. We finish by studying single element extensions, and prove that the chain polynomials of the lattice of flats of single element extensions of Uⁿ_n and U^n-1_n are real-rooted.

Received: November 15, 2023. Accepted: February 15, 2024. Final version: April 1, 2024.

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