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.
and Li, Wei-Tian , TITLE =
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π_link(t) ≤ 1 - t^{-1} - t^{-2}/12 for every t ≥ 2, which determines the order of the gap to the trivial bound 1 - t^{-1} up to a constant factor when paired with Goldwasser's lower bound for prime-power t-1.
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A note on the $t$-partite link problem of F\"uredi
π_link(t) ≤ 1 - t^{-1} - t^{-2}/12 for every t ≥ 2, which determines the order of the gap to the trivial bound 1 - t^{-1} up to a constant factor when paired with Goldwasser's lower bound for prime-power t-1.