A note on squarefree monomial ideals and matroid ports

Abstract

A matroid port is a clutter determined by the circuits of a matroid that contain a fixed point. A monomial ideal associated to a (binary) matroid port can be characterized by using its minimal generators and its minimal prime ideals. In this note we point out this characterization and we demonstrate that any full-supported squarefree monomial ideal is the intersection of finitely many ideals associated to matroid ports. In the binary case, the matroid port decomposition is related to the irredundant primary decomposition of the ideal.