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From polytopes to operads and back (2112.13743v1)
Published 27 Dec 2021 in math.KT and math.CO
Abstract: For a directed polytope, we construct a colored operad whose Poincare-Hilbert series encodes certain operations on the cellular complex of the polytope. We conjecture that for a class of short polytopes the constructed operads are Koszul and self-dual. We verify the conjecture for simplices, polygons, and products thereof.
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