367 citations · 1.6k across the 63 of their papers we have counts for
14 papers · 1 filter
Canonical representatives for divisor classes on tropical curves and the Matrix-Tree Theorem
Yang An, Matthew Baker, Greg Kuperberg +1
Let be a compact tropical curve (or metric graph) of genus . Using the theory of tropical theta functions, Mikhalkin and Zharkov proved that there is a canonical effective r…
Probabilistic existence of regular combinatorial structures
Greg Kuperberg, Shachar Lovett, Ron Peled
We show the existence of regular combinatorial objects which previously were not known to exist. Specifically, for a wide range of the underlying parameters, we show the existence…
Probabilistic existence of rigid combinatorial structures
Greg Kuperberg, Shachar Lovett, Ron Peled
We show the existence of rigid combinatorial objects which previously were not known to exist. Specifically, for a wide range of the underlying parameters, we show the existence of…
Fat 4-polytopes and fatter 3-spheres
David Eppstein, Greg Kuperberg, Günter M. Ziegler
We introduce the fatness parameter of a 4-dimensional polytope P, defined as ϕ(P)=(f_1+f_2)/(f_0+f_3). It arises in an important open problem in 4-dimensional combinatorial geometr…
Kasteleyn cokernels
Greg Kuperberg
We consider Kasteleyn and Kasteleyn-Percus matrices, which arise in enumerating matchings of planar graphs, up to matrix operations on their rows and columns. If such a matrix is d…
Symmetry classes of alternating-sign matrices under one roof
Greg Kuperberg
In a previous article [math.CO/9712207], we derived the alternating-sign matrix (ASM) theorem from the Izergin-Korepin determinant for a partition function for square ice with doma…