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.
Keywords: Riordan number, Riordan path, -avoiding derangement.