The Lexicographic Cross-Section of the Plactic Monoid Is Regular

  • Christian Choffrut
  • Robert Mercaş
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8079)


The plactic monoid is the quotient of the free monoid by the congruence generated by Knuth’s well-celebrated rules. It is well-known that the set of Young tableaux is a cross-section of this congruence which happens to be regular. The main result of this work shows that the set of alphabetically minimal elements in the congruence classes is also regular. We give a full combinatorial characterization of these minimal elements and show that constructing them is as fast as constructing a tableau.


Minimal Element Transitive Closure Young Tableau Congruence Class Free Monoid 
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.


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Christian Choffrut
    • 1
  • Robert Mercaş
    • 2
  1. 1.L.I.A.F.A.Université Paris 7Paris CedexFrance
  2. 2.Institut für InformatikChristian-Albrechts-Universität zu KielKielGermany

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