Ehrhart positivity of all positroids

Establish that every positroid is Ehrhart positive, meaning that all coefficients of the Ehrhart polynomial of its matroid base polytope are nonnegative.

Background

Positroids index cells of the totally nonnegative Grassmannian and include both series-parallel matroids and multi-path matroids. The paper proves Ehrhart positivity for series-parallel matroids and for all series-parallel extensions of multi-path matroids, thereby establishing positivity for substantial subclasses of positroids.

The authors explicitly note that subdivisions of positroid base polytopes into series-parallel matroid base polytopes do not by themselves resolve the broader positroid question, because the paper constructs a connected transversal matroid with a negative Ehrhart coefficient despite such subdivision behavior. Thus positivity for arbitrary positroids remains unresolved.

References

Ferroni, Jochemko, and Schröter conjectured that all positroids are Ehrhart positive Conjecture~6.3.

— Series-parallel extensions and Ehrhart positivity  (2610.03122 - Li et al., 2 Oct 2026) in Section 1, Introduction; Remark 1.1 (remark labeled rem:main-special-cases); Remark 7.1 (remark labeled rem:positroid-subdivision-structure)

A central conjecture of Ferroni, Jochemko, and Schröter posits that every positroid is Ehrhart positive. While Ehrhart positivity has recently been verified for notable classes such as lattice path matroids and series-parallel matroids, the general conjecture remains open.

— Ehrhart positivity for paving positroids  (2610.21501 - Liu et al., 15 Oct 2026) in Abstract and Section 1, Introduction (the Ferroni–Jochemko–Schröter conjecture, cited as Conjecture 6.3)