SIAMDM
2010
13 years 9 months ago
2010
Let g1, . . . , gk be tropical polynomials in n variables with Newton polytopes P1, . . . , Pk. We study combinatorial questions on the intersection of the tropical hypersurfaces d...
DCG
1999
13 years 10 months ago
1999
Monotone path polytopes arise as a special case of the construction of fiber polytopes, introduced by Billera and Sturmfels. A simple example is provided by the permutahedron, whic...
JCT
2002
13 years 10 months ago
2002
In [1], the author generalized Ehrhart's idea ([2]) of counting lattice points in dilated rational polytopes: Given a rational polytope, that is, a polytope with rational vert...
EJC
2000
13 years 10 months ago
2000
For general polytopes, it has turned out that with respect to many questions it su ces to consider only the simple polytopes, i.e., d-dimensional polytopes where every vertex is c...
EJC
2000
13 years 10 months ago
2000
Consider the moment curve in the real Euclidean space Rd defined parametrically by the map : R Rd , t (t) = (t, t2 , . . . , td ). The cyclic d-polytope Cd(t1, . . . , tn) is t...
COMBINATORICS
2004
13 years 10 months ago
2004
Bisztriczky introduced the multiplex as a generalization of the simplex. A polytope is multiplicial if all its faces are multiplexes. In this paper it is proved that the flag vect...
DCG
2007
13 years 10 months ago
2007
The aim of this paper is to initiate the study of alcoved polytopes, which are polytopes arising from affine Coxeter arrangements. This class of convex polytopes includes many clas...
DCG
2007
13 years 10 months ago
2007
We consider polytopes in Rn that are generated by N vectors in Rn whose coordinates are independent subgaussian random variables. (A particular case of such polytopes are symmetri...
COMBINATORICS
2007
13 years 10 months ago
2007
We use methods of combinatorics of polytopes together with geometrical and computational ones to obtain the complete list of compact hyperbolic Coxeter npolytopes with n + 3 facet...
DCG
2006
13 years 10 months ago
2006
Abstract. Hyperbolic area is characterized as the unique continuous isometry invariant simple valuation on convex polygons in H2 . We then show that continuous isometry invariant s...