Séminaire Lotharingien de Combinatoire, 89B.36 (2023), 12 pp.
Luis Ferroni, Jacob P. Matherne, Matthew Stevens and
Lorenzo Vecchi
Hilbert-Poincaré Series of Matroid Chow Rings and Intersection Cohomology
Abstract.
We study the Hilbert-Poincaré series of three algebraic objects arising in the Chow-theoretic and Kazhdan-Lusztig framework of matroids. These are, respectively, the Hilbert-Poincaré series of the Chow ring, the augmented Chow ring, and the intersection cohomology module. We develop and highlight an explicit parallelism between the Kazhdan-Lusztig polynomial of a matroid and the Hilbert-Poincaré series of its Chow ring that extends naturally to the Hilbert-Poincaré series of both the intersection cohomology module and the augmented Chow ring.
Received: November 15, 2022.
Accepted: February 20, 2023.
Final version: April 1, 2023.
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