The h-vector of a positroid is a pure O-sequence. (May 2023)

• Record Type: Journal Article
• Authors: He, Amy; Lai, Pierce; Oh, Suho
• Is Part Of: European journal of combinatorics. Volume 110(2023)
• Publication Date: 2023-05
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2023.103684
• Languages: English
• ISSNs: 0195-6698

Abstract

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.