A New Formula for the Volume of Lattice Polyhedra.
Alexander duality in subdivisions of Lawrence polytopes.
An Ehrhart series formula for reflexive polytopes.
Bounding the degrees of generators of a homogeneous dimension 2 toric ideal.
Combinatorial construction of toric residues.
In this paper we investigate the problem of finding an explicit element whose toric residue is equal to one. Such an element is shown to exist if and only if the associated polytopes are essential. We reduce the problem to finding a collection of partitions of the lattice points in the polytopes satisfying a certain combinatorial property. We use this description to solve the problem when and for any when the polytopes of the divisors share a complete flag of faces. The latter generalizes earlier...
Combinatorial fans, lattice-ordered groups, and their neighbours: A short excursion.
Computing the Ehrhart Polynomial of a Convex Lattice Polytope.
Differential modules defined by systems of equations
Ehrhart clutters: regularity and max-flow min-cut.
Embedding a Polytope in a Lattice.
Flag f-vectors and the cd-index.
Flag vectors of multiplicial polytopes.
Gorenstein polytopes obtained from bipartite graphs.
Gosset polytopes in integral octonions
We study the integral quaternions and the integral octonions along the combinatorics of the -cell, a uniform polytope with the symmetry , and the Gosset polytope with the symmetry . We identify the set of the unit integral octonions or quaternions as a Gosset polytope or a -cell and describe the subsets of integral numbers having small length as certain combinations of unit integral numbers according to the or actions on the or the -cell, respectively. Moreover, we show that each...
Gröbner bases of lattices, corner polyhedra, and integer programming.
-vectors, Eulerian polynomials and stable polytopes of graphs.
Intrinsic Volumes and Lattice Points of Crosspolytopes.
Lattice points in Minkowski sums.
Lattice-Free Polytopes and Their Diameter.
Matroid polytopes, nested sets and Bergman fans.