Introduces Chow functions on posets that parallel KLS functions and relate positivity conjectures on face lattices, matroid Chow rings, and Bruhat intervals.
40 [PP23] Roberto Pagaria and Gian Marco Pezzoli,Hodge theory for polymatroids, Int
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Simplicial spheres without large missing faces satisfy g-number lower bounds in terms of graph independence numbers, including g2 ≥ (1/2 − δ(d))f0 for flag spheres with δ(d) → 0 as d → ∞.
Complete built matroids have γ-positive Chow polynomials with γ-vectors realized as f-vectors of simplicial complexes, yielding new inequalities for the Poincaré polynomial of M-bar_{0,n}.
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Chow functions for partially ordered sets
Introduces Chow functions on posets that parallel KLS functions and relate positivity conjectures on face lattices, matroid Chow rings, and Bruhat intervals.
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Lower bounds on the $g$-numbers of spheres without large missing faces
Simplicial spheres without large missing faces satisfy g-number lower bounds in terms of graph independence numbers, including g2 ≥ (1/2 − δ(d))f0 for flag spheres with δ(d) → 0 as d → ∞.
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Matroid analogues of Gal's conjecture
Complete built matroids have γ-positive Chow polynomials with γ-vectors realized as f-vectors of simplicial complexes, yielding new inequalities for the Poincaré polynomial of M-bar_{0,n}.