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math.CO2021
Freehedra are short
Daria Poliakova
We prove the combinatorial property of shortness for freehedra. Note that associahedra, a sibling family of polytopes, are not short.
math.KT2021
From polytopes to operads and back
Sergey Arkhipov, Daria Poliakova
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 cl…