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Repeated Lefschetz-like decompositions for flag doubly Cohen--Macaulay simplicial complexes and gamma vectors of flag spheres
We find decompositions of $h$-polynomials of flag doubly Cohen--Macaulay simplicial complex that yield a direct connection between gamma vectors of flag spheres and constructions used to build them geometrically. More specifically, they are determined by iterated double suspensions and a ``net nonnegative set of edge subdivisions'' taking it to the …