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The Kazhdan-Lusztig polynomials of uniform matroids.
- Source :
-
Advances in Applied Mathematics . Jan2021, Vol. 122, pN.PAG-N.PAG. 1p. - Publication Year :
- 2021
-
Abstract
- The Kazhdan-Lusztig polynomial of a matroid was introduced by Elias et al. (2016) [4]. Let U m , d denote the uniform matroid of rank d on a set of m + d elements. Gedeon et al. (2017) [7] pointed out that they can derive an explicit formula of the Kazhdan-Lusztig polynomials of U m , d using equivariant Kazhdan-Lusztig polynomials. In this paper we give an alternative explicit formula, which allows us to prove the real-rootedness of the Kazhdan-Lusztig polynomials of U m , d for 2 ≤ m ≤ 15 and all d 's. The case m = 1 was previously proved by Gedeon et al. (2017) [8]. We further determine the Z -polynomials of all U m , d 's and prove the real-rootedness of the Z -polynomials of U m , d for 2 ≤ m ≤ 15 and all d 's. Our formula also enables us to give an alternative proof of Gedeon, Proudfoot, and Young's formula for the Kazhdan-Lusztig polynomials of U m , d 's without using the equivariant Kazhdan-Lusztig polynomials. [ABSTRACT FROM AUTHOR]
- Subjects :
- *POLYNOMIALS
*MATROIDS
*ALGORITHMS
*EVIDENCE
Subjects
Details
- Language :
- English
- ISSN :
- 01968858
- Volume :
- 122
- Database :
- Academic Search Index
- Journal :
- Advances in Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 146736215
- Full Text :
- https://doi.org/10.1016/j.aam.2020.102117