Open problems on k-orbit polytopes
Gabe Cunningham, Daniel Pellicer
TL;DR
This paper presents 35 open problems related to the combinatorial, geometric, and algebraic properties of k-orbit abstract polytopes and introduces a formalized theory of rooted polytopes.
Contribution
It introduces a formalized theory of rooted polytopes and compiles a comprehensive list of open problems in the study of k-orbit abstract polytopes.
Findings
Identification of 35 open problems in k-orbit polytopes
Formalization of the theory of rooted polytopes
Insights into combinatorial, geometric, and algebraic aspects
Abstract
We present 35 open problems on combinatorial, geometric and algebraic aspects of k-orbit abstract polytopes. We also present a theory of rooted polytopes that has appeared implicitly in previous work but has not been formalized before.
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Taxonomy
Topicsgraph theory and CDMA systems · Advanced Combinatorial Mathematics · semigroups and automata theory