On Ranks of Regular Polygons

Abstract

In this paper we study various versions of extension complexity for polygons through the study of factorization ranks of their slack matrices. In particular, we develop a new asymptotic lower bound for their nonnegative rank, decreasing the gap between the current bounds, we introduce a new upper bound for their boolean rank, deriving some numerical evidence for the asymptotic equivalence of the boolean rank of $n$-gons and $\log_2(n)$, and we show the nonmonotonicity of the complex positive semidefinite rank of $n$-gons.