Remarks on Catalan and super-Catalan numbers

• Autorzy: Anna Dorota Krystek , Łukasz Jan Wojakowski
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46L53: Noncommutative probability and statistics
• 46L54: Free probability and free operator algebras
• 60E10: Characteristic functions; other transforms

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2011
• Tom: 96
• Numer: 1
• Strony: 237-244

Daty

wydano

2011

Twórcy

autor

Anna Dorota Krystek

• Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

autor

Łukasz Jan Wojakowski

• Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Identyfikatory

DOI

10.4064/bc96-0-15