Séminaire Lotharingien de Combinatoire, 95B.24 (2026), 12 pp.
Luis Ferroni, Alejandro H. Morales and Greta Panova
Skew Shapes, Ehrhart Positivity and Beyond
Abstract.
A classical result by Kreweras (1965) allows one to compute the number of plane partitions of a given skew shape and bounded parts as certain determinants. We prove that these determinants expand as polynomials with nonnegative coefficients. Our main result has numerous ramifications impacting on several areas within algebraic combinatorics. It can be reformulated in terms of order polynomials of cell posets of skew shapes, and explains important positivity phenomena about the Ehrhart polynomials of matroids, and of order polytopes. Among other applications, we show that all fence posets, including the zig-zag poset, have order polynomials with nonnegative coefficients. We discuss a general method for proving positivity which reduces to showing positivity of the linear terms of the order polynomials.
Received: November 15, 2025.
Accepted: February 15, 2026.
Final version: April 1, 2026.
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