Combinatorics of Riordan arrays with identical \(A\) and \(Z\) sequences. (English) Zbl 1243.05007

Cheon, Gi-Sang; Kim, Hana; Shapiro, Louis W.

Discrete Math. 312, No. 12-13, 2040-2049 (2012).

Summary: In theory, Riordan arrays can have any A-sequence and any Z-sequence. For examples of combinatorial interest they tend to be related. Here we look at the case that they are identical or nearly so. We provide a combinatorial interpretation in terms of weighted Łukasiewicz paths and then look at several large classes of examples.

MSC:

05A05	Permutations, words, matrices
05A15	Exact enumeration problems, generating functions

Keywords:

Riordan array; Łukasiewicz path; Dyck path; consistent Riordan array

Software:

OEIS

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