Archiv der Mathematik

, Volume 101, Issue 5, pp 427–436 | Cite as

Sorting and generating reduced words

  • Olcay Coşkun
  • Müge Taşkın


We introduce a partial order on the set of all reduced words of a given permutation ω, called directed-braid poset of ω. This poset enables us to produce two algorithms: One is a sorting algorithm applied to any reduced word of ω and aims to obtain the natural word (i.e. lexicographically largest reduced word); the other one is a generation algorithm applied to the natural word and returns the set of all reduced words of ω.


Partial Order Generation Algorithm Coxeter Group Lexicographic Order Sort Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Coşkun O., Taşkın M.: Tower Tableaux. J. Combin. Theory Series A 120, 843–871 (2013)CrossRefzbMATHGoogle Scholar
  2. 2.
    A. Garsia, The saga of reduced factorizations of elements of the symmetric group, Publications du LaCIM, Université du Québec a Montréal, Canada, Vol. 29, 2002.Google Scholar
  3. 3.
    D. E. Knuth, The Art of Computer Programming, 3. Sorting and Searching (second ed.), Addison-Wesley, (1998).Google Scholar
  4. 4.
    Stanley R.: On the number of reduced decompositions of elements of Coxeter groups. European J. Combinatorics. 5, 359–372 (1984)CrossRefzbMATHGoogle Scholar
  5. 5.
    Stembridge J.R.: Some combinatorial aspects of reduced words in finite Coxeter groups. Trans. Amer. Math. Soc. 349, 1285–1332 (1997)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Boğaziçi Üniversitesi, Matematik BölümüBebekTurkey

Personalised recommendations