6 citations · 21 across the 22 of their papers we have counts for
23 papers
Toric partial orders
Mike Develin, Matthew Macauley, Victor Reiner
We define toric partial orders, corresponding to regions of graphic toric hyperplane arrangements, just as ordinary partial orders correspond to regions of graphic hyperplane arran…
Discrete bidding games
Mike Develin, Sam Payne
We study variations on combinatorial games in which, instead of alternating moves, the players bid with discrete bidding chips for the right to determine who moves next. We conside…
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…
Ehrhart Polynomial Roots and Stanley's Non-negativity Theorem
Benjamin Braun, Mike Develin
Stanley's non-negativity theorem is at the heart of many of the results in Ehrhart theory. In this paper, we analyze the root behavior of general polynomials satisfying the conditi…
Tropical polytopes and cellular resolutions
Mike Develin, Josephine Yu
Tropical polytopes are images of polytopes in an affine space over the Puiseux series field under the degree map. This viewpoint gives rise to a family of cellular resolutions of m…
Rigidity theory for matroids
Mike Develin, Jeremy L. Martin, Victor Reiner
Combinatorial rigidity theory seeks to describe the rigidity or flexibility of bar-joint frameworks in R^d in terms of the structure of the underlying graph G. The goal of this art…