Journal of Integer Sequences, Vol. 17 (2014), Article 14.7.1

On a New Collection of Words in the Catalan Family

Christian Stump
Institut für Mathematik
Freie Universität Berlin


In this note, we provide a bijection between a new collection of words on nonnegative integers of length n and Dyck paths of length 2n-2, thus proving that this collection belongs to the Catalan family. The surprising key step in this bijection is the zeta map which is an important map in the study of q,t-Catalan numbers. Finally we discuss an alternative approach to this new collection of words using two statistics on planted trees that turn out to be closely related to the Tutte polynomial on the Catalan matroid.

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(Concerned with sequence A000108.)

Received April 7 2014; revised version received May 20 2014. Published in Journal of Integer Sequences, May 20 2014.

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