algebra / Commutative algebra

Log-Concavity of Codimension-Three Pure O-Sequences

For a pure O-sequence $h = (h_0, \dots, h_e)$ of codimension three and type two, is $h_i^2 \ge h_{i-1} h_{i+1}$ for every interior index $i$? The stated monomial case is proved; the broader level-Hilbert-function case remains open.

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algebraMay 21, 2026Significance 10/100Registry: lean verified

Log-Concavity of Codimension-Three Pure O-Sequences

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For a pure O-sequence $h = (h_0, \dots, h_e)$ of codimension three and type two, is $h_i^2 \ge h_{i-1} h_{i+1}$ for every interior index $i$? The stated monomial case is proved; the broader level-Hilbert-function case remains open.

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For a pure O-sequence $h = (h_0, \dots, h_e)$ of codimension three and type two, is $h_i^2 \ge h_{i-1} h_{i+1}$ for every interior index $i$? The stated monomial case is proved; the broader level-Hilbert-function case remains open.

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