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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Incidence toric ideals for t-subsets in k-subsets are interpreted with generators as null t-designs and balanced orientable normal d-pseudomanifolds, with octahedra generators playing a key structural role.
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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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Incidence toric ideals and three-point functions
Incidence toric ideals for t-subsets in k-subsets are interpreted with generators as null t-designs and balanced orientable normal d-pseudomanifolds, with octahedra generators playing a key structural role.