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» Alcoved Polytopes, I
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DCG
2008
110views more  DCG 2008»
13 years 10 months ago
A Centrally Symmetric Version of the Cyclic Polytope
We define a centrally symmetric analogue of the cyclic polytope and study its facial structure. We conjecture that our polytopes provide asymptotically the largest number of faces...
Alexander I. Barvinok, Isabella Novik
FOCS
2006
IEEE
14 years 4 months ago
On a Geometric Generalization of the Upper Bound Theorem
We prove an upper bound, tight up to a factor of 2, for the number of vertices of level at most in an arrangement of n halfspaces in Rd , for arbitrary n and d (in particular, the...
Uli Wagner
DCG
2002
71views more  DCG 2002»
13 years 10 months ago
A Polytope Related to Empirical Distributions, Plane Trees, Parking Functions, and the Associahedron
The volume of the n-dimensional polytope nx := fy 2 Rn : yi 0 and y1 + + yi x1 + + xi for all 1 i ng for arbitrary x := x1; : : : ; xn with xi 0 for all i de nes a polyn...
Richard P. Stanley, Jim Pitman
JCT
2006
89views more  JCT 2006»
13 years 10 months ago
Revlex-initial 0/1-polytopes
We introduce revlex-initial 0/1-polytopes as the convex hulls of reverse-lexicographically initial sets of 0/1-vectors. Thus for each n 2d , we consider the 0/1-knapsack polytope ...
Rafael Gillmann, Volker Kaibel
CC
2004
Springer
115views System Software» more  CC 2004»
14 years 4 months ago
Periodic Polyhedra
This paper presents a new method for computing the integer hull of a parameterized rational polyhedron by introducing the concept of periodic polyhedron. Besides concerning general...
Benoît Meister