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.
Stanley,Hilbert functions of graded algebras
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New upper bounds on Castelnuovo-Mumford regularity of monomial curves are given that are tighter than Lvovsky's bound under specific conditions, using Apery sets and Frobenius numbers, along with algorithms and sumset applications.
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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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New bounds on Castelnuovo--Mumford regularity of monomial curves and application to sumsets
New upper bounds on Castelnuovo-Mumford regularity of monomial curves are given that are tighter than Lvovsky's bound under specific conditions, using Apery sets and Frobenius numbers, along with algorithms and sumset applications.