19 citations · 57 across the 9 of their papers we have counts for
10 papers
Tropical Linear Spaces
David E Speyer
We define tropical analogues of the notions of linear space and Plucker coordinate and study their combinatorics. We introduce tropical analogues of intersection and dualization an…
A Broken Circuit Ring
Nicholas J. Proudfoot, David E. Speyer
Given a matroid M represented by a linear subspace L in n-space (equivalently by an arrangement of n hyperplanes in L), we define a graded ring R(L) which degenerates to the Stanle…
Tropical Mathematics
David Speyer, Bernd Sturmfels
These are the notes for the Clay Mathematics Institute Senior Scholar Lecture which was delivered by Bernd Sturmfels in Park City, Utah, on July 22, 2004. The topic of this lecture…
An arctic circle theorem for groves
T. K. Petersen, D. Speyer
In earlier work, Jockusch, Propp, and Shor proved a theorem describing the limiting shape of the boundary between the uniformly tiled corners of a random tiling of an Aztec diamond…
The Cube Recurrence
Gabriel D. Carroll, David E Speyer
We construct a combinatorial model that is described by the cube recurrence, a nonlinear recurrence relation introduced by Propp, which generates families of Laurent polynomials in…
Perfect Matchings and the Octahedron Recurrence
David E Speyer
We study a recurrence defined on a three dimensional lattice and prove that its values are Laurent polynomials in the initial conditions with all coefficients equal to one. This re…