2008
DOI: 10.1016/j.disc.2007.05.001
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Riordan paths and derangements

Abstract: Riordan paths are Motzkin paths without horizontal steps on the x-axis. We establish a correspondence between Riordan paths and (321, 3142)-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.

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Cited by 5 publications
(5 citation statements)
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“…Now we compute C ∞ (t) by considering the so called "Riordan paths" [32,33] (Motzkin paths [34] with no horizontal steps at the bottom line) weighted through q and r. (see Fig. 3).…”
Section: Autocorrelator At T = ∞mentioning
confidence: 99%
“…Now we compute C ∞ (t) by considering the so called "Riordan paths" [32,33] (Motzkin paths [34] with no horizontal steps at the bottom line) weighted through q and r. (see Fig. 3).…”
Section: Autocorrelator At T = ∞mentioning
confidence: 99%
“…The explicit formula for the kth Riordan numbers is as in Eq. (5) (see [10] for a simple combinatorial proof), and asymptotically r k = Θ * (3 k ).…”
Section: The Order Of the Ring Componentmentioning
confidence: 99%
“…The DB-matching of size k with specified χ and z (the label of the leftmost point on U) will be denoted by DB(k, χ, z). 10 The dual trees of DB-matchings have the following structure (we denote the vertices of D(M ) identically to the corresponding faces of the map of M ): There is a path B 0 D 1 D 2 . .…”
Section: Small Components For Even K (Pairs)mentioning
confidence: 99%
“…2 . The paths with such constraints and j = 0 are known in mathematical literature as Riordan paths (and their multiplicity as Riordan numbers 24 25 26 . For j ≥ 0 these are Riordan arrays 27 , whose generating functions are known to be 27 …”
Section: Resultsmentioning
confidence: 99%