Quotients of uniform positroids (Q2073307)

Summary: Two matroids \(M\) and \(N\) are said to be concordant if there is a strong map from \(N\) to \(M\). This also can be stated by saying that each circuit of \(N\) is a union of circuits of \(M\). In this paper, we consider a class of matroids called positroids, introduced by \textit{A. Postnikov} [in: Proceedings of the international congress of mathematicians 2018, ICM 2018, Rio de Janeiro, Brazil, August 1--9, 2018. Volume IV. Invited lectures. Hackensack, NJ: World Scientific; Rio de Janeiro: Sociedade Brasileira de Matemática (SBM). 3181--3211 (2018; Zbl 1448.05219)], and utilize their combinatorics to determine concordance among some of them. More precisely, given a uniform positroid, we give a purely combinatorial characterization of a family of positroids that is concordant with it. We do this by means of their associated decorated permutations. As a byproduct of our work, we describe completely the collection of circuits of this particular subset of positroids.