2000
DOI: 10.1016/s0012-365x(99)00343-x
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Generating trees and proper Riordan Arrays

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Cited by 53 publications
(40 citation statements)
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“…The correspondence between tennis ball s-sequences and generating trees allows us to use results obtained for these latter combinatorial objects. First of all, we re-introduce from [6] the concept of an AGT matrix. Definition 4.1.…”
Section: The Main Resultsmentioning
confidence: 99%
See 1 more Smart Citation
“…The correspondence between tennis ball s-sequences and generating trees allows us to use results obtained for these latter combinatorial objects. First of all, we re-introduce from [6] the concept of an AGT matrix. Definition 4.1.…”
Section: The Main Resultsmentioning
confidence: 99%
“…This immediately gives d 0 ðtÞ ¼ TðtÞ: The generating function of the other columns is given by the following: Proof. First, we observe that specification (2.2) can be written in the product notation (see [6]): ðkÞ ! Q kþsÀ1 j¼1 ðk þ s À jÞ; s52; and this immediately shows that a node at level n þ 1 with label k þ 2 can be determined from the nodes at level n with label h þ 1;…”
Section: The Main Resultsmentioning
confidence: 99%
“…The group is quite easily developed but unifies many themes in enumeration, including of the generalized concept of Renewal Array defined by Rogers in 1978 ( [28] and [1,[19][20][21], etc.). Their basic idea was to define a class of infinite lower triangular arrays with properties analogous to those those of the Pascal triangle whose elements.…”
Section: Riordan Arrays and Riordan Groupmentioning
confidence: 99%
“…The infinite triangles of Pascal, Catalan, Motzkin and Schröder are important and meaningful examples of pRa's, and many others have been proposed and developed (see, e.g., [10,18,20]). In the recent literature, Riordan arrays have attracted the attention of various authors from many point of view and many examples and applications can be found (see, e.g., [1,6,11,[13][14][15]17,24,21] but the literature is still developing now). In particular, Merlini and Verri [15] pointed out an important connection between pRa's and generating trees and they call proper generating trees the corresponding trees.…”
Section: Introductionmentioning
confidence: 99%
“…In the recent literature, Riordan arrays have attracted the attention of various authors from many point of view and many examples and applications can be found (see, e.g., [1,6,11,[13][14][15]17,24,21] but the literature is still developing now). In particular, Merlini and Verri [15] pointed out an important connection between pRa's and generating trees and they call proper generating trees the corresponding trees. There exists a vast literature about the concept of generating trees: it was used for the first time, without any specific name, by Chung et al [5] and successively by West [22,23].…”
Section: Introductionmentioning
confidence: 99%