The Ehrhart Theory of Matroid Polytopes

Ferroni Rivetti, Luis (2021) The Ehrhart Theory of Matroid Polytopes, [Dissertation thesis], Alma Mater Studiorum Università di Bologna. Dottorato di ricerca in Matematica, 34 Ciclo. DOI 10.48676/unibo/amsdottorato/9945.
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Abstract

In this thesis we investigate the Ehrhart polynomials of the basis polytope and the independence polytope of a matroid. We disprove conjectures by De Loera, Haws and Koppe (2007) and by Castillo and Liu (2015) asserting the positivity of the coefficients of these polynomials. Through the way we prove several positive results such as the Ehrhart positivity of hypersimplices and matroids of rank 2. Also, we provide an explicit formula for the Ehrhart polynomial of the basis polytope and the independence polytope of sparse paving matroids, a class that is conjecturally predominant.

Abstract
Tipologia del documento
Tesi di dottorato
Autore
Ferroni Rivetti, Luis
Supervisore
Dottorato di ricerca
Ciclo
34
Coordinatore
Settore disciplinare
Settore concorsuale
Parole chiave
Ehrhart polynomials, Matroid polytopes, Hypersimplices, Lattice points, Generalized permutohedra
URN:NBN
DOI
10.48676/unibo/amsdottorato/9945
Data di discussione
23 Novembre 2021
URI

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