Linear Systems on Tropical Curves (2009)
Haase, Christian, Musiker, Gregg, Yu, Josephine
A tropical curve \Gamma is a metric graph with possibly unbounded edges, and tropical rational functions are continuous piecewise linear functions with integer slopes. We define the complete linear...
Polar decomposition and Brion’s theorem. (2008)
Abstract. In this note we point out the relation between Brion’s formula for the lattice point generating function of a convex polytope in terms of the vertex cones [Bri88] on the one hand, and the...
Cayley decompositions of lattice polytopes and upper bounds for h^*-polynomials (2008)
Haase, Christian, Nill, Benjamin, Payne, Sam
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 bound as a consequence...
Contemporary Mathematics Problems from the Cottonwood Room. (2008)
Matthias Beck, Beifang Chen, Lenny Fukshansky, Christian Haase, Bruce Reznick, Sinai Robins, ...
Abstract. This collection was compiled by Christian Haase and Bruce Reznick from problems presented at the problem sessions, and submissions solicited from the participants of the AMS/IMS/SIAM summer...
Seit der St. Vincent-Deklaration im Jahre 1989 mit der Zielsetzung, die Qualität der Versorgung schwangerer Diabetikerinnen so zu verbessern, dass sich das Morbiditäts- und Mortalitätsrisiko...
Lattice points in Minkowski sums (2007)
Haase, Christian, Nill, Benjamin, Paffenholz, Andreas, Santos, Francisco
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 smooth and the normal...
Grid graphs, Gorenstein polytopes, and domino stackings (2007)
Beck, Matthias, Haase, Christian, Sam, Steven V.
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 polytopes, and we...
Lattice Polytopes and Triangulations with Applications to Toric Geometry (2007)
Christian Haase, Lattice Polytopes, Christian Alexander Haase, Vom Fachbereich Mathematik, Vorsitzender Prof, ...
ecessary copying power and I was admitted. I started my discrete career in a very stimulating environment: the Berlin discrete community assembled in the graduate school and at the TU--Berlin, and...
Dedekind-Carlitz Polynomials as Lattice-Point Enumerators in Rational Polyhedra (2007)
Beck, Matthias, Haase, Christian, Matthews, Asia R.
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 integers. Carlitz...
Quasi-period collapse and GL_n(Z)-scissors congruence in rational polytopes (2007)
Haase, Christian, McAllister, Tyrrell B.
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 understood, and all...
On permutation polytopes (2007)
Baumeister, Barbara, Haase, Christian, Nill, Benjamin, Paffenholz, Andreas
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 applications we completely...
Groebner Bases for Transportation Polytopes (2006)
Haase, Christian, Paffenholz, Andreas
The toric ideals of $3\times 3$ transportation polytopes $T$ are quadratically generated. The only exception is the Birkhoff polytope $B_3$. If $T$ is not a multiple of $B_3$, these ideals even have...
Lattices generated by skeletons of reflexive polytopes (2005)
Haase, Christian, Nill, Benjamin
Lattices generated by lattice points in skeletons of reflexive polytopes are essential in determining the fundamental group and integral cohomology of Calabi-Yau hypersurfaces. Here we prove that the...
Theorems of Brion, Lawrence, and Varchenko on rational generating functions for cones (2005)
Beck, Matthias, Haase, Christian, Sottile, Frank
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 expository note contains...
Haase, Christian, Kurz, Sascha
We give a construction for the d-dimensional simplices with all distances in {1,2} from the set of partitions of d+1.
Integral affine structures on spheres III: complete intersections (2005)
Haase, Christian, Zharkov, Ilia
We extend our model for affine structures on toric Calabi-Yau hypersurfaces math.AG/0205321 to the case of complete intersections.
We give a construction for the d-dimensional simplices with all distances in {1,2} from the set of partitions of d+1.
Integral affine structures on spheres: complete intersections (2005)
Haase, Christian, Zharkov, Ilia
We give a construction of integral affine structures on spheres which conjecturally arise in the maximal degeneration limits of Calabi-Yau complete intersection families in toric varieties. This...
The reflexive dimension of a lattice polytope (2004)
Haase, Christian, Melnikov, Ilarion V.
The reflexive dimension refldim(P) of a lattice polytope P is the minimal d so that P is the face of some d-dimensional reflexive polytope. We show that refldim(P) is finite for every P, and give...
Lattice polygons and the number 2i+7 (2004)
Haase, Christian, Schicho, Josef
In this note we classify all triples (a,b,i) such that there is a convex lattice polygon P with area a, and b respectively i lattice points on the boundary respectively in the interior. The crucial...
Thesis (Ph.D.)--University of Oxford, 2004.
Christian Haase, Josef Schicho
Abstract. In this note we classify all triples (a, b, i) such that there is a convex lattice polygon P with area a, and p respectively i lattice points on the boundary respectively in the interior....
Polar decomposition and Brion's theorem (2003)
In this note we point out the relation between Brion's formula for the lattice point generating function of a convex polytope in terms of the vertex cones [Brion1988] on the one hand, and the polar...
Haase, Christian, Zharkov, Ilia
This paper is a continuation of our paper math.AG/0205321 where we have built a combinatorial model for the torus fibrations of Calabi-Yau toric hypersurfaces. This part addresses the connection...
Haase, Christian, Zharkov, Ilia
We describe in purely combinatorial terms dual pairs of integral affine structures on spheres which come from the conjectural metric collapse of mirror families of Calabi-Yau toric hypersurfaces. The...
Examples and counterexamples for the Perles conjecture, Discrete Comput (2002)
Christian Haase, Unter M. Ziegler
Abstract. The combinatorial structure of a d-dimensional simple convex polytope | as given, for example, by the set of the (d 1)-regular subgraphs of the facets | can be reconstructed from its...
Examples and counterexamples for the Perles conjecture, Discrete Comput (2002)
Christian Haase, Unter M. Ziegler
Abstract. The combinatorial structure of a d-dimensional simple convex polytope { as given, for example, by the set of the (d 1)-regular subgraphs of the facets { can be reconstructed from its...
Examples and counterexamples for the Perles conjecture, Discrete Comput (2002)
Christian Haase, G Unter, M. Ziegler
Abstract. The combinatorial structure of a d{dimensional simple convex polytope { as given, for example, by the set of the (d 1){regular subgraphs of facets { can be reconstructed from its abstract...
All toric local complete intersection singularities admit projective crepant resolutions (2001)
Dais, Dimitrios I., Haase, Christian, Ziegler, Günter M.
It is known that the underlying spaces of all abelian quotient singularities which are embeddable as complete intersections of hypersurfaces in an affine space can be overall resolved by means of...
Examples and counterexamples for Perles' conjecture (2000)
Haase, Christian, Ziegler, Günter M.
The combinatorial structure of a d-dimensional simple convex polytope can be reconstructed from its abstract graph [Blind & Mani 1987, Kalai 1988]. However, no polynomial/efficient algorithm is known...
Leipzig, Universiẗat, Diss., 2000.
All Toric L.C.I.-Singularities Admit Projective Crepant Resolutions (1999)
Dimitrios I. Dais, Christian Haase, Günter M. Ziegler, G Unter, M. Ziegler
. It is known that the underlying spaces of all abelian quotient singularities which are embeddable as complete intersections of hypersurfaces in an aÆne space can be overall resolved by means of...
On the Maximal Width of Empty Lattice Simplices (1999)
Christian Haase, Günter M. Ziegler
We construct d-dimensional empty lattice simplices of arbitrarily high volume from (d-1)-dimensional ones...
All toric l.c.i.-singularities admit projective crepant resolutions (1998)
Dais, Dimitrios I., Haase, Christian, Ziegler, G"unter M.
It is known that the underlying spaces of all abelian quotient singularities which are embeddable as complete intersections of hypersurfaces in an affine space can be overall resolved by means of...
All Toric L.C.I.-Singularities Admit Projective Crepant Resolutions (1998)
Dimitrios I. Dais, Christian Haase, Günter M. Ziegler
It is known that the underlying spaces of all abelian quotient singularities which are embeddable as complete intersections of hypersurfaces in an aÆne space can be overall resolved by means of...
Thesis (doctoral)--Christian-Albrechts-Universität zu Kiel, 1994.
Mikrofiche-Ausg.: 2 Mikrofiches : 24x