DIAMETERS OF GRAPHS OF REDUCED WORDS AND RANK-TWO ROOT SUBSYSTEMS
We study the diameter of the graph G(w) of reduced words of an element w in a Coxeter group W whose edges correspond to applications of the Coxeter relations. We resolve conjectures of Reiner-Roichman [Trans. Amer. Math. Soc. 365 (2013), pp. 2279-2802] and Dahlberg-Kim [Diameters of graphs on reduce...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
American Mathematical Society
2022
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| Online Access: | View Fulltext in Publisher |
| Summary: | We study the diameter of the graph G(w) of reduced words of an element w in a Coxeter group W whose edges correspond to applications of the Coxeter relations. We resolve conjectures of Reiner-Roichman [Trans. Amer. Math. Soc. 365 (2013), pp. 2279-2802] and Dahlberg-Kim [Diameters of graphs on reduced words of 12 and 21-inflations, arXiv:2010.15758, 2020] by proving a tight lower bound on this diameter when W = Sn is the symmetric group and by characterizing the equality cases. We also give partial results in other classical types which illustrate the limits of current techniques. © 2022 American Mathematical Society. |
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| ISBN: | 00029939 (ISSN) |
| DOI: | 10.1090/proc/15912 |