Generalized asymptotic Euler's relation for certain families of polytopes
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.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2008
- DOI:
- 10.48550/arXiv.0809.0088
- arXiv:
- arXiv:0809.0088
- Bibcode:
- 2008arXiv0809.0088M
- Keywords:
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- Mathematics - Combinatorics;
- 68R05
- E-Print:
- 6 pages