Riordan Paths and Derangements

Details Riordan Paths and Derangements Riordan Paths and Derangements

2006-02-14

arxiv.org/abs/math/0602298v1

Mathematics

Combinatorics

9 pages, 2 figures

Scientific paper

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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