Classical combinatorial concepts

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


In this chapter we begin by defining partially ordered sets, linear extensions, the dual of a poset, and the disjoint union of two posets. We then define further combinatorial objects we will need including compositions, partitions, diagrams and Young tableaux, reverse tableaux, Young’s lattice and Schensted insertion.

Key words

compositions diagrams partially ordered sets partitions tableaux Schensted insertion Young’s lattice 


  1. 31.
    Fulton, W.: Young tableaux. With applications to representation theory and geometry. Cambridge University Press, Cambridge (1997)Google Scholar
  2. 34.
    Gelfand, I., Krob, D., Lascoux, A., Leclerc, B., Retakh, V., Thibon, J.-Y.: Noncommutative symmetric functions. Adv. Math. 112, 218–348 (1995)Google Scholar
  3. 40.
    Haglund, J., Luoto, K., Mason, S., van Willigenburg, S.: Quasisymmetric Schur functions. J. Combin. Theory Ser. A 118, 463–490 (2011)Google Scholar
  4. 72.
    Sagan, B.: The symmetric group. Representations, combinatorial algorithms, and symmetric functions. Second edition. Springer-Verlag, New York (2001)Google Scholar
  5. 81.
    Stanley, R.: Enumerative combinatorics. Vol. 2. Cambridge University Press, Cambridge (1999)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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