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- W2034762331 abstract "In the present paper, we consider the statistic “number of udu's” in Dyck paths. The enumeration of Dyck paths according to semilength and various other parameters has been studied in several papers. However, the statistic “number of udu's” has been considered only recently. Let Dn denote the set of Dyck paths of semilength n and let Tn,k, Ln,k, Hn,k and Wn,k(r) denote the number of Dyck paths in Dn with k udu's, with k udu's at low level, at high level, and at level r⩾2, respectively. We derive their generating functions, their recurrence relations and their explicit formulas. A new setting counted by Motzkin numbers is also obtained. Several combinatorial identities are given and other identities are conjectured." @default.
- W2034762331 created "2016-06-24" @default.
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- W2034762331 date "2004-10-01" @default.
- W2034762331 modified "2023-09-27" @default.
- W2034762331 title "The statistic “number of udu's” in Dyck paths" @default.
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- W2034762331 doi "https://doi.org/10.1016/j.disc.2004.07.002" @default.
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