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01128nam a2200145Ia 4500 |
| 001 |
10.1090-proc-15912 |
| 008 |
220706s2022 CNT 000 0 und d |
| 020 |
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|a 00029939 (ISSN)
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| 245 |
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|a DIAMETERS OF GRAPHS OF REDUCED WORDS AND RANK-TWO ROOT SUBSYSTEMS
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| 260 |
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|b American Mathematical Society
|c 2022
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| 856 |
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|z View Fulltext in Publisher
|u https://doi.org/10.1090/proc/15912
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| 520 |
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|a 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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| 700 |
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|a Gaetz, C.
|e author
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|a Gao, Y.
|e author
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| 773 |
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|t Proceedings of the American Mathematical Society
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