2021
DOI: 10.1016/j.aam.2020.102117
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The Kazhdan-Lusztig polynomials of uniform matroids

Abstract: Motivated by the concepts of the inverse Kazhdan-Lusztig polynomial and the equivariant Kazhdan-Lusztig polynomial, Proudfoot defined the equivariant inverse Kazhdan-Lusztig polynomial for a matroid. In this paper, we show that the equivariant inverse Kazhdan-Lusztig polynomial of a matroid is very useful for determining its equivariant Kazhdan-Lusztig polynomials, and we determine the equivariant inverse Kazhdan-Lusztig polynomials for Boolean matroids and uniform matroids. As an application, we give a new pr… Show more

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Cited by 11 publications
(16 citation statements)
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“…Given a fixed m, d, and i, the value of the coefficient is invariant of selection of CH so long as |CH| remains the same. This formula has already inspired other mathematical results since the posting of this paper [12,13].…”
Section: Introductionmentioning
confidence: 73%
See 2 more Smart Citations
“…Given a fixed m, d, and i, the value of the coefficient is invariant of selection of CH so long as |CH| remains the same. This formula has already inspired other mathematical results since the posting of this paper [12,13].…”
Section: Introductionmentioning
confidence: 73%
“…After their introduction, these polynomials quickly drew active research interest due to their conjectured properties such as the non-negativity of coefficients, and real-rootedness (see [10,14,15,33]). These are natural properties to be curious about in light of what we know for the original Kazhdan-Lusztig polynomials.…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…Of course an analogous (but a bit more complicated) formula holds for P M using the results of [11]. Also, there exist upper-bounds for λ that are good enough to show the positivity of the expression above with little effort.…”
Section: Lemma 51 a Matroid M On E Of Rank K Is Sparse Paving If And ...mentioning
confidence: 98%
“…It is computationally expensive to calculate them explicitly using their defining recurrence. For some particular families of matroids such as uniform matroids [11,12], wheels and whirls [18] and other graphic matroids [14], it is possible to derive concrete and explicit formulas. Although these particular cases are interesting, the number of matroids belonging to each of these classes is almost negligible within the family of all matroids.…”
Section: Luis Ferroni and Lorenzo Vecchimentioning
confidence: 99%