Frobenius identities for the volume map on Cohen-Macaulay rings give sufficient conditions for anisotropy and Hard Lefschetz in Gorenstein quotients and deduce the g-theorem for simplicial spheres plus the Ohsugi-Hibi conjecture.
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4 Pith papers cite this work. Polarity classification is still indexing.
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Iterated power set applications generate a hierarchy of operads linking the permutative operad to triassociative, substitution, and composition operads, plus a new operad on relative simplicial complexes governed by join polyhedral products.
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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Frobenius identities for the volume map on Cohen--Macaulay rings
Frobenius identities for the volume map on Cohen-Macaulay rings give sufficient conditions for anisotropy and Hard Lefschetz in Gorenstein quotients and deduce the g-theorem for simplicial spheres plus the Ohsugi-Hibi conjecture.
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Power set operads
Iterated power set applications generate a hierarchy of operads linking the permutative operad to triassociative, substitution, and composition operads, plus a new operad on relative simplicial complexes governed by join polyhedral products.
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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.