Depth in Coxeter groups of type B

Eli Bagno, Riccardo Biagioli, Mordechai Novick

Research output: Contribution to journalConference articlepeer-review


The depth statistic was defined for every Coxeter group in terms of factorizations of its elements into product of reflections. Essentially, the depth gives the minimal path cost in the Bruaht graph, where the edges have prescribed weights. We present an algorithm for calculating the depth of a signed permutation which yields a simple formula for this statistic. We use our algorithm to characterize signed permutations having depth equal to length. These are the fully commutative top-and-bottom elements defined by Stembridge. We finally give a characterization of the signed permutations in which the reflection length coincides with both the depth and the length.

Original languageEnglish
Pages (from-to)913-924
Number of pages12
JournalDiscrete Mathematics and Theoretical Computer Science
StatePublished - 2015
Externally publishedYes
Event27th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2015 - Daejeon, Korea, Republic of
Duration: 6 Jul 201510 Jul 2015

Bibliographical note

Publisher Copyright:
© 2015 Discrete Mathematics and Theoretical Computer Science (DMTCS), Nancy, France.


  • Bruhat graph
  • Coxeter groups
  • Depths
  • Length
  • Reflections


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