Algebraic Combinatorics

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CRC Press, Apr 1, 1993 - Mathematics - 368 pages
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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.
 

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Contents

The Matchings Polynomial
1
The Characteristic Polynomial
19
Formal Power Series and Generating Functions
37
Quotients of Graphs
75
Matchings and Walks
93
Pfaffians
113
Orthogonal Polynomials
131
Moment Sequences
149
DistanceRegular Graphs
195
Association Schemes
221
Representations of DistanceRegular Graphs
261
Polynomial Spaces
285
Q Polynomial Spaces
307
Tight Designs
333
Terminology
353
Index
359

Strongly Regular Graphs
177

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Popular passages

Page 331 - P. Delsarte, Four fundamental parameters of a code and their combinatorial significance, Info.
Page 331 - P. Delsarte, J.-M. Goethals and JJ Seidel, Spherical codes and designs, Geom. Dedicata 6 (1977) 363-388.

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