4 citations · 8 across the 8 of their papers we have counts for
6 papers · 1 filter
Mirković-Vilonen Polytopes from Combinatorics
Mario Sanchez
Mirković-Vilonen (MV) polytopes are a class of generalized permutahedra originating from geometric representation theory. In this paper we study MV polytopes coming from matroid po…
Lattice Path Delta Matroids
Douglas M. Chen, Mario Sanchez, John Veliz +1
We initiate the study of a type generalization of the lattice path matroids defined by Bonin, de Mier, and Noy. These are delta matroids whose feasible sets are in bijection…
Coxeter tournaments
Brett Kolesnik, Mario Sanchez
We describe the Coxeter permutahedra, recently studied by Ardila, Castillo, Eur and Postnikov, in terms of random Coxeter tournaments, which involve cooperative and solitaire games…
Valuations and the Hopf Monoid of Generalized Permutahedra
Federico Ardila, Mario Sanchez
The goal of this paper is to show that valuation theory and Hopf theory are compatible on the class of generalized permutahedra. We prove that the Hopf structure on…
The geometry of random tournaments
Mario Sanchez, Brett Kolesnik
A tournament is an orientation of a graph. Each edge represents a match, directed towards the winner. The score sequence lists the number of wins by each team. Landau (1953) charac…
The Universal Valuation of Coxeter Matroids
Christopher Eur, Mario Sanchez, Mariel Supina
Coxeter matroids generalize matroids just as flag varieties of Lie groups generalize Grassmannians. Valuations of Coxeter matroids are functions that behave well with respect to su…