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.
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