36 citations · 171 across the 32 of their papers we have counts for
27 papers · 1 filter
Fine Polyhedral Adjunction Theory
Sofía Garzón Mora, Christian Haase
Originally introduced by Fine and Reid in the study of plurigenera of toric hypersurfaces, the Fine interior of a lattice polytope got recently into the focus of research. It is ha…
Competitive equilibrium always exists for combinatorial auctions with graphical pricing schemes
Marie-Charlotte Brandenburg, Christian Haase, Ngoc Mai Tran
We show that a competitive equilibrium always exists in combinatorial auctions with anonymous graphical valuations and pricing, using discrete geometry. This is an intuitive and ea…
Ehrhart-equivalent -polytopes are equidecomposable
Jakob Erbe, Christian Haase, Francisco Santos
We show that if two lattice -polytopes and have the same Ehrhart function then they are -equidecomposable; that is, they can be partit…
Levelness of Order Polytopes
Christian Haase, Florian Kohl, Akiyoshi Tsuchiya
Since their introduction by Stanley~\cite{StanleyOrderPoly} order polytopes have been intriguing mathematicians as their geometry can be used to examine (algebraic) properties of f…
Smooth centrally symmetric polytopes in dimension 3 are IDP
Matthias Beck, Christian Haase, Akihiro Higashitani +4
In 1997 Oda conjectured that every smooth lattice polytope has the integer decomposition property. We prove Oda's conjecture for centrally symmetric -dimensional polytopes, by s…
Discrete Mixed Volume and Hodge-Deligne Numbers
Sandra Di Rocco, Christian Haase, Benjamin Nill
Generalizing the famous Bernstein-Kushnirenko Theorem, Khovanskii proved in 1978 a combinatorial formula for the arithmetic genus of the compactification of a generic complete inte…
The Finiteness Threshold Width of Lattice Polytopes
Mónica Blanco, Christian Haase, Jan Hofmann +1
We prove that in each dimension there is a constant such that for every all but finitely many -polytopes with lattice point…
Mixed Ehrhart polynomials
Christian Haase, Martina Juhnke-Kubitzke, Raman Sanyal +1
For lattice polytopes , Bihan (2014) introduced the discrete mixed volume in analogy to the classical mixed vo…
Face-subgroups of permutation polytopes
Christian Haase
In [Baumeister, H., Nill, Paffenholz, On permutation polytopes, Adv. Math. 222 (2009), 431-452 / arXiv:0709.1615] we conjectured a characterization of subgroups H of a permutation…
Convex-normal (pairs of) polytopes
Christian Haase, Jan Hofmann
In 2012 Gubeladze (Adv.\ Math.\ 2012) introduced the notion of k-convex-normal polytopes to show that integral polytopes all of whose edges are longer than 4d(d+1) have the integer…
Existence of unimodular triangulations - positive results
Christian Haase, Andreas Paffenholz, Lindsay C. Piechnik +1
Unimodular triangulations of lattice polytopes arise in algebraic geometry, commutative algebra, integer programming and, of course, combinatorics. In this article, we review sever…
Polytopes associated to Dihedral Groups
Barbara Baumeister, Christian Haase, Benjamin Nill +1
In this note we investigate the convex hull of those -permutation matrices that correspond to symmetries of a regular -gon. We give the complete facet description. A…
Integer decomposition property of dilated polytopes
David A. Cox, Christian Haase, Takayuki Hibi +1
Let be an integral convex polytope of dimension and write , where , for dilations of . We say t…
Permutation Polytopes of Cyclic Groups
Barbara Baumeister, Christian Haase, Benjamin Nill +1
We investigate the combinatorics and geometry of permutation polytopes associated to cyclic permutation groups, i.e., the convex hulls of cyclic groups of permutation matrices. We…
Polyhedral adjunction theory
Sandra Di Rocco, Christian Haase, Benjamin Nill +1
In this paper we give a combinatorial view on the adjunction theory of toric varieties. Inspired by classical adjunction theory of polarized algebraic varieties we define two conve…
Cayley decompositions of lattice polytopes and upper bounds for h^*-polynomials
Christian Haase, Benjamin Nill, Sam Payne
We give an effective upper bound on the h^*-polynomial of a lattice polytope in terms of its degree and leading coefficient, confirming a conjecture of Batyrev. We deduce this boun…
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…
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…
Groebner Bases for Transportation Polytopes
Christian Haase, Andreas Paffenholz
The toric ideals of transportation polytopes are quadratically generated. The only exception is the Birkhoff polytope . If is not a multiple of , thes…
Lattices generated by skeletons of reflexive polytopes
Christian Haase, Benjamin Nill
Lattices generated by lattice points in skeletons of reflexive polytopes are essential in determining the fundamental group and integral cohomology of Calabi-Yau hypersurfaces. Her…
A bijection between the d-dimensional simplices with distances in {1,2} and the partitions of d+1
Christian Haase, Sascha Kurz
We give a construction for the d-dimensional simplices with all distances in {1,2} from the set of partitions of d+1.
Theorems of Brion, Lawrence, and Varchenko on rational generating functions for cones
Matthias Beck, Christian Haase, Frank Sottile
We discuss and give elementary proofs of results of Brion and of Lawrence-Varchenko on the lattice-point enumerator generating functions for polytopes and cones. This largely expos…