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arXiv · 1909.09888

Kazhdan-Lusztig polynomials of matroids under deletion

Tom Braden·Artem Vysogorets
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Abstract

We present a formula which relates the Kazhdan-Lusztig polynomial of a matroid $M$, as defined by Elias, Proudfoot and Wakefield, to the Kazhdan--Lusztig polynomials of the matroid obtained by deleting an element, and various contractions and localizations of $M$. We give a number of applications of our formula to Kazhdan--Lusztig polynomials of graphic matroids, including a simple formula for the Kazhdan--Lusztig polynomial of a parallel connection graph.

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Tom Braden, Artem Vysogorets. 2023-06-11. Kazhdan-Lusztig polynomials of matroids under deletion. https://arxiv.org/abs/1909.09888

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