Generalized asymptotic Euler's relation for certain families of polytopes
Combinatorics
2011-07-11 v3
Abstract
According to Euler's relation any polytope P has as many faces of even dimension as it has faces of odd dimension. As a generalization of this fact one can compare the number of faces whose dimension is congruent to i modulo m with the number of all faces of P for some positive integer m and for some 0 < i < m+1. We show some classes of polytopes for which the above proportion is asymptotically equal to 1/m.
Keywords
Cite
@article{arxiv.0809.0088,
title = {Generalized asymptotic Euler's relation for certain families of polytopes},
author = {Laszlo Major},
journal= {arXiv preprint arXiv:0809.0088},
year = {2011}
}
Comments
6 pages; added section