Combinatorial Polytope Enumeration
Combinatorics
2009-08-13 v1
Abstract
We describe a provably complete algorithm for the generation of a tight, possibly exact superset of all combinatorially distinct simple n-facet polytopes in R^d, along with their graphs, f-vectors, and face lattices. The technique applies repeated cutting planes and planar sweeps to a d-simplex. Our generator has implications for several outstanding problems in polytope theory, including conjectures about the number of distinct polytopes, the edge expansion of polytopal graphs, and the d-step conjecture.
Keywords
Cite
@article{arxiv.0908.1619,
title = {Combinatorial Polytope Enumeration},
author = {Sandeep Koranne and Anand Kulkarni},
journal= {arXiv preprint arXiv:0908.1619},
year = {2009}
}