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Composition tableaux and further combinatorial concepts

  • Kurt Luoto
  • Stefan Mykytiuk
  • Stephanie van Willigenburg
Chapter
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Abstract

In order to state results in the next chapter, we extend many definitions from Chapter 2 to define composition diagrams, Young composition tableaux that correspond to Young tableaux, and the Young composition poset. We additionally define reverse composition diagrams, reverse composition tableaux that correspond to reverse tableaux, and the reverse composition poset. Finally, useful bijections between Young tableaux, Young composition tableaux, reverse tableaux and reverse composition tableaux are described.

Key words

composition tableaux reverse composition poset reverse composition tableaux tableaux bijections Young composition poset Young composition tableaux 

References

  1. 15.
    Bessenrodt, C., Luoto, K., van Willigenburg, S.: Skew quasisymmetric Schur functions and noncommutative Schur functions. Adv. Math. 226, 4492–4532 (2011)Google Scholar
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    Haglund, J., Luoto, K., Mason, S., van Willigenburg, S.: Quasisymmetric Schur functions. J. Combin. Theory Ser. A 118, 463–490 (2011)Google Scholar
  3. 64.
    Mason, S.: A decomposition of Schur functions and an analogue of the Robinson-Schensted-Knuth algorithm. Sém. Lothar. Combin. 57, Art. B57e, 24 pp (2006/08)Google Scholar

Copyright information

© Kurt Luoto, Stefan Mykytiuk, Stephanie van Willigenburg 2013

Authors and Affiliations

  • Kurt Luoto
    • 1
  • Stefan Mykytiuk
    • 2
  • Stephanie van Willigenburg
    • 1
  1. 1.Department of MathematicsUniversity of British ColumbiaVancouverCanada
  2. 2.Department of Mathematics and StatisticsYork UniversityTorontoCanada

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