The Riordan Group and Applications by Shapiro, Louis; Sprugnoli, Renzo; Barry, Paul;

Series: Springer Monographs in Mathematics;

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Product details:

Edition number 1st ed. 2022
Publisher Springer
Date of Publication 29 April 2022
Number of Volumes 1 pieces, Book

ISBN 9783030941505
Binding Hardback
No. of pages362 pages
Size 235x155 mm
Weight 740 g
Language English
Illustrations 13 Illustrations, black & white; 6 Illustrations, color

Short description:

The ever-growing applications and richness of approaches to the Riordan group is captured in this comprehensive monograph, authored by those who are among the founders and foremost world experts in this field. The concept of a Riordan array has played a unifying role in enumerative combinatorics over the last three decades. The Riordan arrays and Riordan group is a new growth point in mathematics that is both being influenced by, and continuing its contributions to, other fields such as Lie groups, elliptic curves, orthogonal polynomials, spline functions, networks, sequences and series, Beal conjecture, Riemann hypothesis, to name several. In recent years the Riordan group has made links to quantum field theory and has become a useful tool for computer science and computational chemistry. We can look forward to discovering further applications to unexpected areas of research. Providing a baseline and springboard to further developments and study, this book may also serve as a text for anyone interested in discrete mathematics, including combinatorics, number theory, matrix theory, graph theory, and algebra.

Long description:

The ever-growing applications and richness of approaches to the Riordan group is captured in this comprehensive monograph, authored by those who are among the founders and foremost world experts in this field. The concept of a Riordan array has played a unifying role in enumerative combinatorics over the last three decades. The Riordan arrays and Riordan group is a new growth point in mathematics that is both being influenced by, and continuing its contributions to, other fields such as Lie groups, elliptic curves, orthogonal polynomials, spline functions, networks, sequences and series, Beal conjecture, Riemann hypothesis, to name several. In recent years the Riordan group has made links to quantum field theory and has become a useful tool for computer science and computational chemistry. We can look forward to discovering further applications to unexpected areas of research. Providing a baseline and springboard to further developments and study, this book may also serve asa text for anyone interested in discrete mathematics, including combinatorics, number theory, matrix theory, graph theory, and algebra.

?Each chapter ends with a set of exercises, designed to help the reader to develop a deeper understanding of the theory and methods of Riordan arrays, and a reference section. Solutions to selected exercises are also provided at the end of the book. It is a pleasure to read such a comprehensive and clearly written book on Riordan arrays and the Riordan group. This book excellently introduces and develops a fascinating new research area of enumerative combiatronics.? (Chen Sheng, zbMATH 1498.05002, 2022)

1 Introduction.- 2 Extraction of coefficients and generating functions.- 3 The Riordan group.- 4 Characterization of Riordan arrays by special sequences.- 5 Combinatorial sums and inversions.- 6 Generalized Riordan arrays.- 7 Extensions of the Riordan group.- 8 q-analogs of Riordan arrays.- 9 Orthogonal polynomials. Solutions.- Index.