4 citations · 9 across the 3 of their papers we have counts for
6 papers
Coefficients and Roots of Ehrhart Polynomials
M. Beck, J. A. De Loera, M. Develin +2
The Ehrhart polynomial of a convex lattice polytope counts integer points in integral dilates of the polytope. We present new linear inequalities satisfied by the coefficients of E…
Vertices of Gelfand-Tsetlin Polytopes
Jesús A. De Loera, Tyrrell B. McAllister
This paper is a study of the polyhedral geometry of Gelfand-Tsetlin patterns arising in the representation theory $\mathfrak{gl}_n \C$ and algebraic combinatorics. We present a com…
Short Rational Functions for Toric Algebra and Applications
Jesus De Loera, David Haws, Raymond Hemmecke +3
We encode the binomials belonging to the toric ideal associated with an integral matrix using a short sum of rational functions as introduced by Barvinok \ci…
Polyhedral Cones of Magic Cubes and Squares
M. Ahmed, J. De Loera, R. Hemmecke
Using computational algebraic geometry techniques and Hilbert bases of polyhedral cones we derive explicit formulas and generating functions for the number of magic squares and mag…
Algebraic Unimodular Counting
Jesus A. De Loera, Bernd Sturmfels
We study algebraic algorithms for expressing the number of non-negative integer solutions to a unimodular system of linear equations as a function of the right hand side. Our metho…
The Complexity of Finding Small Triangulations of Convex 3-Polytopes
Alexander Below, Jesús A. De Loera, Jürgen Richter-Gebert
The problem of finding a triangulation of a convex three-dimensional polytope with few tetrahedra is proved to be NP-hard. We discuss other related complexity results.