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math.CO2026
Singular Hodge theory for combinatorial geometries
Tom Braden, June Huh, Jacob P. Matherne +2
We introduce the intersection cohomology module of a matroid and prove that it satisfies Poincaré duality, the hard Lefschetz theorem, and the Hodge-Riemann relations. As applicat…
math.CO2025
Inverse Kazhdan-Lusztig polynomials of matroids under deletion
Tom Braden, Luis Ferroni, Jacob P. Matherne +1
We provide a deletion formula for the inverse Kazhdan--Lusztig polynomial and the inverse -polynomial of a matroid. Our formulas provide analogues to the deletion formulas of Br…