Fence complexes are associated to positroid varieties, shown to be balls with matching Ehrhart and Hilbert polynomials, and positroid varieties degenerate to reduced unions of toric varieties corresponding to the complexes.
On the Charney–Davis and Neggers–Stanley conjectures.Journal of Com- binatorial Theory, Series A, 109(2):247–280, 2005
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Proves the conjecture that Ehrhart h*-polynomials of order polytopes of generalized snake posets are real-rooted by connecting them to non-nesting rook polynomials.
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Fence Complexes and Toric Degenerations of Positroid Varieties
Fence complexes are associated to positroid varieties, shown to be balls with matching Ehrhart and Hilbert polynomials, and positroid varieties degenerate to reduced unions of toric varieties corresponding to the complexes.
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Order polytopes of generalized snake posets are $h^*$-real-rooted
Proves the conjecture that Ehrhart h*-polynomials of order polytopes of generalized snake posets are real-rooted by connecting them to non-nesting rook polynomials.