Lower bounds for simplicial covers and triangulations of cubes

Adam Bliss; Francis Edward Su

Lower bounds for simplicial covers and triangulations of cubes

Combinatorics 2007-05-23 v1 Metric Geometry

Authors: Adam Bliss , Francis Edward Su

Abstract

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.

Cite

@article{arxiv.math/0310142,
  title  = {Lower bounds for simplicial covers and triangulations of cubes},
  author = {Adam Bliss and Francis Edward Su},
  journal= {arXiv preprint arXiv:math/0310142},
  year   = {2007}
}

Comments

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

Lower bounds for simplicial covers and triangulations of cubes

Abstract

Cite

Comments

Related papers