Lower bounds for simplicial covers and triangulations of cubes

被引：16

作者：

Bliss, A ^{[1
]}

Su, FE ^{[1
]}

机构：

[1] Harvey Mudd Coll, Dept Math, Claremont, CA 91711 USA

来源：

DISCRETE & COMPUTATIONAL GEOMETRY | 2005年 / 33卷 / 04期

关键词：

D O I：

10.1007/s00454-004-1128-0

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

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.

引用

页码：669 / 686

页数：18

共 14 条

[1] Minimal simplicial dissections and triangulations of convex 3-polytopes [J].