Generic and special constructions of pure O-sequences

TL;DR

This paper demonstrates that the h-vectors of certain classes of matroids' Stanley-Reisner rings are pure O-sequences, expanding understanding of their algebraic and combinatorial properties.

Contribution

It identifies three specific classes of matroids whose h-vectors are pure O-sequences, providing new insights into their structure and implications for Stanley's conjecture.

Findings

h-vectors of matroids that are truncations are pure O-sequences

h-vectors of matroids with duals that are (rank+2)-partite are pure O-sequences

matroids of Cohen-Macaulay type at most five have pure O-sequence h-vectors

Abstract

It is shown that the h-vectors of Stanley-Reisner rings of three classes of matroids are pure O-sequences. The classes are (a) matroids that are truncations of other matroids, or more generally of Cohen-Macaulay complexes, (b) matroids whose dual is (rank + 2)-partite, and (c) matroids of Cohen-Macaulay type at most five. Consequences for the computational search for a counterexample to a conjecture of Stanley are discussed.