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Ehrhart positivity for lattice path matroids
Luis Ferroni, Alejandro H. Morales, Greta Panova
We prove that all lattice path matroids are Ehrhart positive. This unifies and generalizes numerous results on the Ehrhart positivity of matroids developed over the last two decade…
Computation and sampling for Schubert specializations
David Anderson, Greta Panova, Leonid Petrov
We present computational results on principal specializations of Schubert polynomials, which count reduced pipe dreams and reduced bumpless pipe dreams (RBPD)…
Skew shapes, Ehrhart positivity and beyond
Luis Ferroni, Alejandro H. Morales, Greta Panova
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 dete…
Preservation of log-concavity on gamma polynomials
Luis Ferroni, Greta Panova, Lorenzo Venturello
Every symmetric polynomial with center of symmetry can be expressed as a linear combination in the basis . The -polynomial of , which we deno…
Hook-length Formulas for Skew Shapes via Contour Integrals and Vertex Models
Greta Panova, Leonid Petrov
The number of standard Young tableaux of a skew shape can be computed as a sum over excited diagrams inside . Excited diagrams are in bijection with certain lozenge tiling…
Minimal skew semistandard tableaux and the Hillman--Grassl correspondence
Alejandro H. Morales, Greta Panova, GaYee Park
Standard tableaux of skew shape are fundamental objects in enumerative and algebraic combinatorics and no product formula for the number is known. In 2014, Naruse gave a formula (N…