This graduate level text is distinguished both by the range of
topics and the novelty of the material it treats--more than half of
the material in it has previously only appeared in research papers.
The first half of this book introduces the characteristic and
matchings polynomials of a graph. It is instructive to consider
these polynomials together because they have a number of properties
in common. The matchings polynomial has links with a number of
problems in combinatorial enumeration, particularly some of the
current work on the combinatorics of orthogonal polynomials. This
connection is discussed at some length, and is also in part the
stimulus for the inclusion of chapters on orthogonal polynomials
and formal power series. Many of the properties of orthogonal
polynomials are derived from properties of characteristic
polynomials. The second half of the book introduces the theory of
polynomial spaces, which provide easy access to a number of
important results in design theory, coding theory and the theory of
association schemes. This book should be of interest to second year
graduate text/reference in mathematics.
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