Lower bounds for simplicial covers and triangulations of cubes

Details Lower bounds for simplicial covers and triangulations of cubes Lower bounds for simplicial covers and triangulations of cubes

2003-10-10

arxiv.org/abs/math/0310142v1

Discrete Comput. Geom. 33 (2005), 669--686

Mathematics

Combinatorics

17 pages, related work at http://www.math.hmc.edu/~su/papers.html

Scientific paper

We show that the size of a minimal simplicial cover of a polytope $P$ is a lower bound for the size of a minimal triangulation of $P$, including ones with extra vertices. We then use this fact to study minimal triangulations of cubes, and we improve lower bounds for covers and triangulations in dimensions 4 through at least 12 (and possibly more dimensions as well). Important ingredients are an analysis of the number of exterior faces that a simplex in the cube can have of a specified dimension and volume, and a characterization of corner simplices in terms of their exterior faces.

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