5 papers
Lagrangian combinatorics of matroids
Federico Ardila, Graham Denham, June Huh
The Lagrangian geometry of matroids was introduced in [ADH20] through the construction of the conormal fan of a matroid M. We used the conormal fan to give a Lagrangian-geometric i…
A semi-small decomposition of the Chow ring of a matroid
Tom Braden, June Huh, Jacob P. Matherne +2
We give a semi-small orthogonal decomposition of the Chow ring of a matroid M. The decomposition is used to give simple proofs of Poincaré duality, the hard Lefschetz theorem, and…
Logarithmic concavity of Schur and related polynomials
June Huh, Jacob P. Matherne, Karola Mészáros +1
We show that normalized Schur polynomials are strongly log-concave. As a consequence, we obtain Okounkov's log-concavity conjecture for Littlewood-Richardson coefficients in the sp…
Logarithmic concavity for morphisms of matroids
Christopher Eur, June Huh
Morphisms of matroids are combinatorial abstractions of linear maps and graph homomorphisms. We introduce the notion of basis for morphisms of matroids, and show that its generatin…
Hodge-Riemann relations for Potts model partition functions
Petter Brändén, June Huh
We prove that the Hessians of nonzero partial derivatives of the (homogenous) multivariate Tutte polynomial of any matroid have exactly one positive eigenvalue on the positive orth…