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Panhandle matroids are a specific family of lattice-path matroidscorresponding to panhandle-shaped Ferrers diagrams. Their matroid polytopes arethe subpolytopes carved from a hypersimplex to form matroid polytopes of pavingmatroids. It has been an active area of research to determine which families ofmatroid polytopes are Ehrhart positive. We prove Ehrhart positivity forpanhandle matroid polytopes, thus confirming a conjecture of Hanely, Martin,McGinnis, Miyata, Nasr, Vindas-Mel\'endez, and Yin (2023). Another standingconjecture posed by Ferroni (2022) asserts that the coefficients of the Ehrhartpolynomial of a connected matroid are bounded above by those of thecorresponding uniform matroid. We prove Ferroni's conjecture for pavingmatroids -- a class conjectured to asymptotically contain all matroids. Theseresults follow from purely enumerative statements, the main one beingconjectured by Hanely et. al concerning the enumeration of a certain class ofordered chain forests. %Thus, the contents and proofs in this paper are mainlyof enumerative combinatorics flavor, with the primary motivation coming fromEhrhart theory. Thus, the content and proofs in this paper reflect anenumerative combinatorics perspective, driven by considerations in Ehrharttheory.

Ehrhart Bounds for Panhandle and Paving Matroids Through Enumeration of Chain Forests