English

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

R2 v1 2026-06-21T11:15:21.821Z