Paul Barry: Riordan Arrays: A Primer



There is a companion website for the book, where beginners can get an idea of Riordan arrays.

Paul Barry was born in Dublin in 1952, and was educated at O'Connells School, Dublin, before obtaining his primary degree in mathematics at Trinity College, Dublin. Subsequent qualifications were gained in the University of Bordeaux and University College, Cork. He has worked at the Ecole Normale Superieure, Tunisia, at University College, Dublin, and from 1981 to his retirement in 2014, he worked in the Institute of Technology, Waterford, where he was lecturer, Head of Department of Computing, Mathematics and Physics, and Head of School of Science, as well as Vice President of International Relations. He continues to work at WIT in an emeritus capacity. His research centres on integer sequences and Riordan arrays.
About the book: The primary goal of this text is to introduce the beginner to the theory of Riordan arrays. Starting in a simple and constructive manner, the basic structure of a Riordan array is explained with clear examples, before a more theoretical grounding is provided. Ordinary Riordan arrays and exponential Riordan arrays are examined, with many explicit examples, and their applications to combinatorics and other areas are explored. In addition, a variety of subgroups of the Riordan group are explored. The production matrix of a Riordan array is shown to play a key role, along with various sequence characterizations.

Formal prerequisites are kept to a minimum, in order to provide a gentle introduction to this exciting area, that involves linear algebra, group theory and algebra, and combinatorics. The reader will be well positioned to further explore the topic of Riordan arrays and their applications, and to undertake projects of their own. They will join a community of interested mathematicians that now spans all continents, in a growing area of research and application that is the subject of an annual international conference.

Download slides of a lecture by the author, giving a brief history of Riordan arrays.(pdf, 3.1Mb)

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