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.

Result

Proved

Status

Resolved

AI contribution

AI-discovered

Method

Argument

Field

Commutative algebra

Posed by

—

Year posed

2022

Years open

4y

Solved

2026-05-21

Model

AlphaProof Nexus

Vendor

Google DeepMind

Collaborators

—

Verification

Lean-verified

Publication

Preprint

Significance

10 / 100*

Disclosed cost

—

Wikipedia

No dedicated article