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