Riordan Paths and Derangements

William Y.C. Chen, Eva Y.P. Deng and Laura L.M. Yang

  Abstract:  Riordan paths are Motzkin paths without horizontal steps on the x-axis. We establish a correspondence between Riordan paths and -avoiding derangements. We also present a combinatorial proof of a recurrence relation for the Riordan numbers in the spirit of the Foata-Zeilberger proof of a recurrence relation on the Schröder numbers.

  AMS Classification:   05A15, 05A19

  Keywords:   Riordan number, Riordan path, -avoiding derangement

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