Combinatorial Polytope Enumeration
Sandeep Koranne, Anand Kulkarni

TL;DR
This paper introduces a provably complete algorithm for generating all combinatorially distinct simple polytopes in R^d, providing valuable tools for solving longstanding problems in polytope theory.
Contribution
It presents a novel algorithm that generates a tight superset of simple polytopes using cutting planes and planar sweeps, advancing polytope enumeration methods.
Findings
Algorithm is provably complete and exact.
Enables exploration of polytope enumeration conjectures.
Impacts understanding of polytope graph properties.
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.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Markov Chains and Monte Carlo Methods · Limits and Structures in Graph Theory
