Log-concave Gorenstein sequences

TL;DR

This paper proves that certain algebraic sequences called Artinian Gorenstein and level sequences are log-concave in specific codimensions, revealing both universal properties and exceptions.

Contribution

It establishes log-concavity for codimension three Artinian Gorenstein sequences and identifies exceptions in codimension four, advancing understanding of algebraic sequence properties.

Findings

Codimension three Artinian Gorenstein sequences are log-concave.

Not all codimension four Artinian Gorenstein sequences are log-concave.

All level sequences in codimension two are log-concave.

Abstract

We show here that codimension three Artinian Gorenstein sequences are log-concave, and that there are codimension four Artinian Gorenstein sequences that are not log-concave. We also show that all level sequences in codimension two, and every compressed level Hilbert function in any codimension is log-concave.