6 papers
Equivariant log concavity and representation stability
Jacob P. Matherne, Dane Miyata, Nicholas Proudfoot +1
We expand upon the notion of equivariant log concavity, and make equivariant log concavity conjectures for Orlik--Solomon algebras of matroids, Cordovil algebras of oriented matroi…
Counting linear extensions of posets with determinants of hook lengths
Alexander Garver, Stefan Grosser, Jacob P. Matherne +1
We introduce a class of posets, which includes both ribbon posets (skew shapes) and -complete posets, such that their number of linear extensions is given by a determinant of a…
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…
Matroid-minor Hopf algebra: a cancellation-free antipode formula and other applications of sign-reversing involutions
Eric Bucher, Chris Eppolito, Jaiung Jun +1
In this paper, we give a cancellation-free antipode formula for the matroid-minor Hopf algebra. We then explore applications of this formula. For example, the cancellation-free for…
Combinatorics of Fourier transforms for type A quiver representations
Pramod N. Achar, Maitreyee C. Kulkarni, Jacob P. Matherne
We describe two new combinatorial algorithms (using the language of "triangular arrays") for computing the Fourier transforms of simple perverse sheaves on the moduli space of repr…