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 → ∞.
Proves gamma-positivity for Hilbert-Poincaré polynomials of Chow rings of matroids with complete and flag building sets, yielding combinatorial analogues of classical positivity conjectures and an explicit simplicial complex realizing the gamma-vector.
citing papers explorer
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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
Proves gamma-positivity for Hilbert-Poincaré polynomials of Chow rings of matroids with complete and flag building sets, yielding combinatorial analogues of classical positivity conjectures and an explicit simplicial complex realizing the gamma-vector.