Contraction and restriction of positroids in terms of decorated permutations

TL;DR

This paper explores how contraction and restriction operations on positroids can be understood through their associated decorated permutations, providing a combinatorial perspective on these matroid transformations.

Contribution

It introduces a method to describe contraction and restriction of positroids using decorated permutations, linking matroid operations to permutation combinatorics.

Findings

Provides a combinatorial framework for positroid operations

Establishes a bijection between positroid transformations and decorated permutations

Enhances understanding of positroid structure in Grassmannian cells

Abstract

A positroid is a matroid defined by Postnikov to study the cells in the non-negative part of the Grassmannian. They are in bijection with decorated permutations. We show a way to explain contraction and restriction of positroids in terms of decorated permutations.