4 citations · 8 across the 8 of their papers we have counts for
9 papers
Permutahedra, Lusztig varieties, degenerations, and subdivisions
Allen Knutson, Mario Sanchez, Melissa Sherman-Bennett
We present an embedded (in ) degeneration of Lusztig varieties (which generalize type Hessenberg varieties) to certain unions of Richardson varieties, giving a simultaneou…
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…
Derived Categories of Permutahedral and Stellahedral Varieties
Mario Sanchez
We utilize the coherent-constructible correspondence to construct full strongly exceptional collections of nef line bundles in the derived category of a toric variety through the c…
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…
Dependent Random Graphs and Multiparty Pointer Jumping
Joshua Brody, Mario Sanchez
We initiate a study of a relaxed version of the standard Erdos-Renyi random graph model, where each edge may depend on a few other edges. We call such graphs "dependent random grap…