Sparse paving positroids

John Machacek; George Nasr

doi:10.63151/amjc.v5i.42

Authors

John Machacek Hampden-Sydney College
George Nasr Augustana University

DOI:

https://doi.org/10.63151/amjc.v5i.42

Keywords:

positroid, sparse paving matroid, Le-diagram, Grassmann necklace, decorated permutation

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.

Sparse paving positroids

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