Equivariant Kazhdan-Lusztig polynomials of thagomizer matroids
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- by Matthew H. Y. Xie and Philip B. Zhang PDF
- Proc. Amer. Math. Soc. 147 (2019), 4687-4695 Request permission
Abstract:
The equivariant Kazhdan-Lusztig polynomial of a matroid was introduced by Gedeon, Proudfoot, and Young. Gedeon conjectured an explicit formula for the equivariant Kazhdan-Lusztig polynomials of thagomizer matroids with an action of symmetric groups. In this paper, we discover a new formula for these polynomials which is related to the equivariant Kazhdan-Lusztig polynomials of uniform matroids. Based on our new formula, we confirm Gedeon’s conjecture by the Pieri rule.References
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Additional Information
- Matthew H. Y. Xie
- Affiliation: College of Science, Tianjin University of Technology, Tianjin 300384, People’s Republic of China
- MR Author ID: 1066556
- Email: xie@mail.nankai.edu.cn
- Philip B. Zhang
- Affiliation: College of Mathematical Science, Tianjin Normal University, Tianjin 300387, People’s Republic of China
- MR Author ID: 1066440
- Email: zhang@tjnu.edu.cn
- Received by editor(s): February 4, 2019
- Received by editor(s) in revised form: February 26, 2019
- Published electronically: June 10, 2019
- Additional Notes: This work was supported by the National Science Foundation of China (Nos. 11701424, 11801447).
The second author is the corresponding author - Communicated by: Yuan Xu
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 4687-4695
- MSC (2010): Primary 05B35, 05E05, 20C30
- DOI: https://doi.org/10.1090/proc/14608
- MathSciNet review: 4011505