Remarks on Catalan and super-Catalan numbers

Volume 96 / 2011

Anna Dorota Krystek, Łukasz Jan Wojakowski Banach Center Publications 96 (2011), 237-244 MSC: 46L53, 46L54, 60E10. DOI: 10.4064/bc96-0-15

Abstract

In this article we discuss the Catalan and super-Catalan (or Schröder) numbers. We start with some combinatorial interpretations of those numbers. We study two probability measures in the context of free probability, one whose moments are super-Catalan, and another, whose even moments are super-Catalan and odd moments are zero. With the use of the latter we also show some new formulae for evaluation of the Catalans in terms of super-Catalans and vice-versa.

Authors

  • Anna Dorota KrystekMathematical Institute, University of Wrocław
    pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
    e-mail
  • Łukasz Jan WojakowskiMathematical Institute, University of Wrocław
    pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
    e-mail

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