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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Diameter of graphs of reduced words and galleries


Authors: Victor Reiner and Yuval Roichman
Journal: Trans. Amer. Math. Soc. 365 (2013), 2779-2802
MSC (2010): Primary 20F55, 20F05
Published electronically: November 26, 2012
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Abstract: For finite reflection groups of types $ A$ and $ B$, we determine the diameter of the graph whose vertices are reduced words for the longest element and whose edges are braid relations. This is deduced from a more general theorem that applies to supersolvable hyperplane arrangements.


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Additional Information

Victor Reiner
Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Email: reiner@math.umn.edu

Yuval Roichman
Affiliation: Department of Mathematics, Bar-Ilan University, 52900 Ramat-Gan, Israel
Email: yuvalr@math.biu.ac.il

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05719-9
PII: S 0002-9947(2012)05719-9
Keywords: Coxeter group, reduced words, supersolvable, hyperplane arrangement, weak order, reflection order, cellular string, zonotope, monotone path, diameter
Received by editor(s): June 28, 2011
Received by editor(s) in revised form: October 5, 2011
Published electronically: November 26, 2012
Additional Notes: The first author was supported by NSF grant DMS–0245379.
The second author was supported in part by the Israel Science Foundation grant # 947/04.
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.