Positroids, Dressian and stable polynomials

Abstract

Our work is motivated by the connection established between Lorentzian polynomials and the Dressian in the seminal work of Br\"and\'en and Huh on Lorentzian polynomials. We analyze this relation for the class of positroids, and are able to show that in this case, we can relate a multiaffine homogenous stable polynomial to it. Additionally, we also highlight that a conjecture for matroids posed by Br\"and\'en and Huh is true when considered over the class of Rayleigh matroids which strictly contain the class of positroids. We collect these findings along with other results for further exploration.