Sparse Paving Positroids

TL;DR

This paper classifies sparse paving positroids using combinatorial tools, enabling their enumeration and revealing connections to sequences involving the golden ratio and Lucas numbers.

Contribution

It introduces a classification method for sparse paving positroids and links their enumeration to well-known mathematical sequences.

Findings

Enumeration of sparse paving positroids

Connection to sequences involving the golden ratio

Relation to Lucas numbers

Abstract

Using Postnikov's Le-diagrams, decorated permutations, and Grassmann necklaces, we classify which positroids are sparse paving matroids. This allows us to enumerate sparse paving positroids, making connections to a known sequence involving the golden ratio and to the Lucas numbers.