36 citations · 171 across the 32 of their papers we have counts for
5 papers · 1 filter
Lattice points in Minkowski sums
Christian Haase, Benjamin Nill, Andreas Paffenholz +1
Fakhruddin has proved that for two lattice polygons P and Q any lattice point in their Minkowski sum can be written as a sum of a lattice point in P and one in Q, provided P is smo…
Grid graphs, Gorenstein polytopes, and domino stackings
Matthias Beck, Christian Haase, Steven V. Sam
We examine domino tilings of rectangular boards, which are in natural bijection with perfect matchings of grid graphs. This leads to the study of their associated perfect matching…
Dedekind-Carlitz Polynomials as Lattice-Point Enumerators in Rational Polyhedra
Matthias Beck, Christian Haase, Asia R. Matthews
We study higher-dimensional analogs of the Dedekind-Carlitz polynomials c(u,v;a,b) := sum_{k=1..b-1} u^[ka/b] v^(k-1), where u and v are indeterminates and a and b are positive int…
Quasi-period collapse and GL_n(Z)-scissors congruence in rational polytopes
Christian Haase, Tyrrell B. McAllister
Quasi-period collapse occurs when the Ehrhart quasi-polynomial of a rational polytope has a quasi-period less than the denominator of that polytope. This phenomenon is poorly under…
On permutation polytopes
Barbara Baumeister, Christian Haase, Benjamin Nill +1
A permutation polytope is the convex hull of a group of permutation matrices. In this paper we investigate the combinatorics of permutation polytopes and their faces. As applicatio…