Paul Barry:
Riordan Arrays: A Primer
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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)
Updated 10-3-2022
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