22 citations · 66 across the 15 of their papers we have counts for
16 papers · 1 filter
Staircase skew Schur functions are Schur P-positive
Federico Ardila, Luis G. Serrano
We prove Stanley's conjecture that, if delta_n is the staircase shape, then the skew Schur functions s_{delta_n / mu} are non-negative sums of Schur P-functions. We prove that the…
Combinatorics and geometry of power ideals
Federico Ardila, Alexander Postnikov
We investigate ideals in a polynomial ring which are generated by powers of linear forms. Such ideals are closely related to the theories of fat point ideals, Cox rings, and box sp…
Tropical hyperplane arrangements and oriented matroids
Federico Ardila, Mike Develin
We study the combinatorial properties of a tropical hyperplane arrangement. We define tropical oriented matroids, and prove that they share many of the properties of ordinary orien…
Pruning Processes and a New Characterization of Convex Geometries
Federico Ardila, Elitza Maneva
We provide a new characterization of convex geometries via a multivariate version of an identity that was originally proved by Maneva, Mossel and Wainwright for certain combinatori…
Transversal and cotransversal matroids via the Lindstrom lemma
Federico Ardila
It is known that the duals of transversal matroids are precisely the strict gammoids. The purpose of this short note is to show how the Lindstrom-Gessel-Viennot lemma gives a simpl…
Flag arrangements and triangulations of products of simplices
Federico Ardila, Sara Billey
We investigate the line arrangement that results from intersecting d complete flags in C^n. We give a combinatorial description of the matroid T_{n,d} that keeps track of the linea…