Kazhdan-Lusztig Polynomials of Matroids Under Deletion

  • Tom Braden
  • Artem Vysogorets


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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