The [formula omitted]-vector of a positroid is a pure O-sequence

Abstract

A well-known conjecture of Stanley is that the h-vector of any matroid is a pure O-sequence. There have been numerous papers with partial progress on this conjecture, but it is still wide open. Positroids are a special class of linear matroids that play a crucial role in the field of total positivity. In this short note, we prove that Stanley’s conjecture holds for positroids.