Riordan Paths and Derangements

William Y. C. Chen; Eva Y. P. Deng; Laura L. M. Yang

Riordan Paths and Derangements

Combinatorics 2007-05-23 v1

Authors: William Y. C. Chen , Eva Y. P. Deng , 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 $(321,3\bar{1}42)$ -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.

Keywords

dyck paths

Cite

@article{arxiv.math/0602298,
  title  = {Riordan Paths and Derangements},
  author = {William Y. C. Chen and Eva Y. P. Deng and Laura L. M. Yang},
  journal= {arXiv preprint arXiv:math/0602298},
  year   = {2007}
}

Comments

9 pages, 2 figures

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