Examples of non-symmetric K\"ahler-Einstein toric Fano manifolds (2009)
Nill, Benjamin, Paffenholz, Andreas
In this note we report on examples of 7- and 8-dimensional toric Fano manifolds that are not symmetric and still admit a Kaehler-Einstein metric. This answers a question first posed by V.V. Batyrev...
Polymake and Lattice Polytopes (2009)
Joswig, Michael, Müller, Benjamin, Paffenholz, Andreas
The polymake software system deals with convex polytopes and related objects from geometric combinatorics. This note reports on a new implementation of a subclass for lattice polytopes. The features...
DOI: 10.1007/s00454-004-1144-0 Geometry (2008)
Springer Science+business Media, Bier Spheres, Anders Björner, Andreas Paffenholz, Jonas Sjöstr, Günter M. Ziegler
Abstract. In 1992 Thomas Bier presented a strikingly simple method to produce a huge number of simplicial (n −2)-spheres on 2n vertices, as deleted joins of a simplicial complex on n vertices with...
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...
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...
Constructions for 4-Polytopes and the Cone of Flag Vectors (2005)
Paffenholz, Andreas, Werner, Axel
We describe a construction for d-polytopes generalising the well known stacking operation. The construction is applied to produce 2-simplicial and 2-simple 4-polytopes with g_2=0 on any number of n...
New polytopes from products (2004)
We construct a new 2-parameter family E_mn of self-dual 2-simple and 2-simplicial 4-polytopes, with flexible geometric realisations. E_44 is the 24-cell. For large m,n the f-vectors have ``fatness''...
Bier Spheres and Posets (2004)
Anders Björner, Anders Bj Orner, Jonas Sjöstrand, Andreas Paffenholz, Jonas Sj Ostrand, Günter M. Ziegler, ...
In 1992 Thomas Bier presented a strikingly simple method to produce a huge number of simplicial (n 2)-spheres on 2n vertices as deleted joins of a simplicial complex on n vertices with its...
New polytopes from products (2004)
Abstract. We construct a new 2-parameter family Emn, m, n ≥ 3, of self-dual 2-simple and 2-simplicial 4-polytopes, with flexible geometric realisations. E44 is the 24-cell. For large m, n the...
Bier spheres and posets (2003)
Björner, Anders, Paffenholz, Andreas, Sjöstrand, Jonas, Ziegler, Günter M.
In 1992 Thomas Bier presented a strikingly simple method to produce a huge number of simplicial (n-2)-spheres on 2n vertices as deleted joins of a simplicial complex on n vertices with its...
The $E_t$-Construction for Lattices, Spheres and Polytopes (2003)
Paffenholz, Andreas, Ziegler, Günter M.
We describe and analyze a new construction that produces new Eulerian lattices from old ones. It specializes to a construction that produces new strongly regular cellular spheres (whose face lattices...