Journal of Integer Sequences, Vol. 9 (2006), Article 06.1.5

Statistics on Dyck Paths


Toufik Mansour
Department of Mathematics
University of Haifa
31905 Haifa
Israel

and

Center for Combinatorics
LPMC
Nan'kai University
Tianjin 300071
P. R. China

Abstract: In this paper we consider several statistics on the set of Dyck paths. Enumeration of Dyck paths according to length and various other parameters has been studied in several papers. However, the statistic "number of udu's" has been considered only recently. We generalize this statistic and derive an explicit formula for the number of Dyck paths of length 2n according to the statistic "number of uu ... udu's" ("number of udud... udu's"). As a consequence, we derive several known results, as well as many new results.

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(Concerned with sequences A000108 A001006 A002054 A078481 and A105633 .)

Received October 2 2005; revised version received January 16 2006. Published in Journal of Integer Sequences January 17 2006.

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