Positroids and Schubert matroids

2008/03/07 by Suho Oh, Oh, Suho · 2 citations
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.0803.1018

openalex publication_date 2008/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Postnikov gave a combinatorial description of the cells in a totally-nonnegative Grassmannian. These cells correspond to a special class of matroids called positroid. We prove his conjecture that a positroid is exactly an intersection of permuted Schubert matroids. This leads to a nice combinatorial description of positroids that is easily computable.

Cited by

• Excluding a line from positroids
• Positroidal aspects of non-nesting rook placements

Related

• Computing positroid cells in the Grassmannian of lines, their boundaries and their intersections
• Contraction and restriction of positroids in terms of decorated permutations
• The facets of the matroid polytope and the independent set polytope of a positroid
• Quotients of uniform positroids
• A representation-theoretic interpretation of positroid classes