Riordan arrays, generalized Narayana triangles, and series reversion

Paul Barry

doi:10.1016/j.laa.2015.10.032

Riordan arrays, generalized Narayana triangles, and series reversion

Paul Barry

School of Science and Computing

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

Using elements of the group of Riordan arrays we define a family of generalized Narayana triangles and their associated generalized Catalan numbers, and study their links to series reversion. In particular we use Lagrange inversion techniques to determine the generating functions for these generalized Catalan numbers.

Original language	English
Pages (from-to)	343-385
Number of pages	43
Journal	Linear Algebra and Its Applications
Volume	491
DOIs	https://doi.org/10.1016/j.laa.2015.10.032
Publication status	Published - 15 Feb 2016

Keywords

Catalan numbers
Lagrange inversion
Narayana numbers
Riordan array

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10.1016/j.laa.2015.10.032

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title = "Riordan arrays, generalized Narayana triangles, and series reversion",

abstract = "Using elements of the group of Riordan arrays we define a family of generalized Narayana triangles and their associated generalized Catalan numbers, and study their links to series reversion. In particular we use Lagrange inversion techniques to determine the generating functions for these generalized Catalan numbers.",

keywords = "Catalan numbers, Lagrange inversion, Narayana numbers, Riordan array",

author = "Paul Barry",

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AU - Barry, Paul

PY - 2016/2/15

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AB - Using elements of the group of Riordan arrays we define a family of generalized Narayana triangles and their associated generalized Catalan numbers, and study their links to series reversion. In particular we use Lagrange inversion techniques to determine the generating functions for these generalized Catalan numbers.

KW - Catalan numbers

KW - Lagrange inversion

KW - Narayana numbers

KW - Riordan array

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U2 - 10.1016/j.laa.2015.10.032

DO - 10.1016/j.laa.2015.10.032

M3 - Article

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EP - 385

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -

Riordan arrays, generalized Narayana triangles, and series reversion

Abstract

Keywords

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