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Every regular polytope has the remarkable property that it inherits all symmetries of each of its facets. This property distinguishes a natural class of polytopes which are called hereditary. Regular ...
We give a realization of the infinity crystal for affine sl(2) using decorated polygons. The construction and proof are combinatorial, making use of Kashiwara and Saito's characterization of the infin...
Given positive integers $d$ and $n$ with $n \geq d+1$, the existence of a normal integral cyclic polytope of dimension $d$ with $n$ vertices is proved. In addition, we show that, for any integers $d \...
Inscribing a regular octahedron into polytopes
inscribed polytopes spheric geometry Combinatorics
2011/9/19
Abstract: We prove that any simple polytope (and some non-simple polytopes) in $\mathbb R^3$ admits an inscribed regular octahedron.
Sherali-Adams Relaxations of Graph Isomorphism Polytopes
Sherali-Adams Relaxations Graph Isomorphism Polytopes Combinatorics
2011/8/24
Abstract: We investigate the Sherali-Adams lift & project hierarchy applied to a graph isomorphism polytope whose integer points encode the isomorphisms between two graphs. In particular, the Sherali-...
Realizability of Polytopes as a Low Rank Matrix Completion Problem
Realizability of Polytopes Low Rank Matrix Completion Problem
2011/2/22
Here we show that the problem of realizing a polytope with specified combinatorics is equivalent to a low rank matrix completion problem.This is comparable to known results reducing realizability to s...