Riordan Paths and Derangements
classification
🧮 math.CO
keywords
pathsriordanderangementsnumbersproofrecurrencerelationavoiding
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Riordan paths are Motzkin paths without horizontal steps on the x-axis. We establish a correspondence between Riordan paths and $(321,3\bar{1}42)$-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 Schr\"oder numbers.
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