Diameter of graphs of reduced words and galleries

Victor Reiner, Yuval Roichman

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)2779-2802
Number of pages24
JournalTransactions of the American Mathematical Society
Issue number5
StatePublished - 2013


  • Cellular string
  • Coxeter group
  • Diameter
  • Hyperplane arrangement
  • Monotone path
  • Reduced words
  • Reflection order
  • Supersolvable
  • Weak order
  • Zonotope


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