Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Equivariant Kazhdan-Lusztig polynomials of thagomizer matroids


Authors: Matthew H. Y. Xie and Philip B. Zhang
Journal: Proc. Amer. Math. Soc. 147 (2019), 4687-4695
MSC (2010): Primary 05B35, 05E05, 20C30
DOI: https://doi.org/10.1090/proc/14608
Published electronically: June 10, 2019
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 05B35, 05E05, 20C30

Retrieve articles in all journals with MSC (2010): 05B35, 05E05, 20C30


Additional Information

Matthew H. Y. Xie
Affiliation: College of Science, Tianjin University of Technology, Tianjin 300384, People’s Republic of China
Email: xie@mail.nankai.edu.cn

Philip B. Zhang
Affiliation: College of Mathematical Science, Tianjin Normal University, Tianjin 300387, People’s Republic of China
Email: zhang@tjnu.edu.cn

DOI: https://doi.org/10.1090/proc/14608
Keywords: Thagomizer matroid, uniform matroid, equivariant Kazhdan-Lusztig polynomial, Pieri rule, plethysm
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
Article copyright: © Copyright 2019 American Mathematical Society