Generalized asymptotic Euler's relation for certain families of polytopes

Details Generalized asymptotic Euler's relation for certain families of polytopes Generalized asymptotic Euler's relation for certain families of polytopes

2008-08-30

arxiv.org/abs/0809.0088v3

Mathematics

Combinatorics

6 pages; added section

Scientific paper

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.

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