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.