Rayleigh Property of Lattice Path Matroids

Abstract

In this work, we studied the class of lattice path matroids $\mathcal{L}$, which was first introduced by J.E. Bonin. A.D. Mier, and M. Noy in [\ref{Bonin 2002}]. Lattice path matroids are transversal, and $\mathcal{L}$ is closed under duals and minors, which in general the class of transversal matroids is not. We give a combinatorial proof of the fact that lattice path matroids are Rayleigh. In addition, this leads us to several research directions, such as which positroids are Rayleigh and which subclass of lattice path matroids are strongly Rayleigh.