A New Formula for the Volume of Lattice Polyhedra.
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Displaying 1 – 20 of 62
Alexander duality in subdivisions of Lawrence polytopes.
Santos, Francisco, Sturmfels, Bernd (2003)
Advances in Geometry
An Ehrhart series formula for reflexive polytopes.
Braun, Benjamin (2006)
The Electronic Journal of Combinatorics [electronic only]
Bounding the degrees of generators of a homogeneous dimension 2 toric ideal.
Hugh Thomas (2002)
Collectanea Mathematica
Combinatorial construction of toric residues.
Amit Khetan, Ivan Soprounov (2005)
Annales de l’institut Fourier
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.
Marra, Vincenzo, Mundici, Daniele (2002)
Séminaire Lotharingien de Combinatoire [electronic only]
Computing the Ehrhart Polynomial of a Convex Lattice Polytope.
A.I. Barvinok (1994)
Discrete & computational geometry
Differential modules defined by systems of equations
Alan Adolphson, Steven Sperber (1996)
Rendiconti del Seminario Matematico della Università di Padova
Ehrhart clutters: regularity and max-flow min-cut.
Martínez-Bernal, José, O'Shea, Edwin, Villarreal, Rafael H. (2010)
The Electronic Journal of Combinatorics [electronic only]
Embedding a Polytope in a Lattice.
H. Maehara (1995)
Discrete & computational geometry
Flag f-vectors and the cd-index.
Richard P. Stanley (1994)
Mathematische Zeitschrift
Flag vectors of multiplicial polytopes.
Bayer, Margaret M. (2004)
The Electronic Journal of Combinatorics [electronic only]
Gorenstein polytopes obtained from bipartite graphs.
Tagami, Makoto (2010)
The Electronic Journal of Combinatorics [electronic only]
Gosset polytopes in integral octonions
Woo-Nyoung Chang, Jae-Hyouk Lee, Sung Hwan Lee, Young Jun Lee (2014)
Czechoslovak Mathematical Journal
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.
Sturmfels, Bernd, Weismantel, Robert, Ziegler, Günter M. (1995)
Beiträge zur Algebra und Geometrie
-vectors, Eulerian polynomials and stable polytopes of graphs.
Athanasiadis, Christos A. (2004)
The Electronic Journal of Combinatorics [electronic only]
Intrinsic Volumes and Lattice Points of Crosspolytopes.
Ulrich Betke, Martin Henk (1993)
Monatshefte für Mathematik
Lattice points in Minkowski sums.
Haase, Christian, Nill, Benjamin, Paffenholz, Andreas, Santos, Francisco (2008)
The Electronic Journal of Combinatorics [electronic only]
Lattice-Free Polytopes and Their Diameter.
M. Deza, S. Onn (1995)
Discrete & computational geometry
Matroid polytopes, nested sets and Bergman fans.
Feichtner, Eva Maria, Sturmfels, Bernd (2005)
Portugaliae Mathematica. Nova Série
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