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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