Algebraic CombinatoricsCRC Press, 1 abr 1993 - 368 páginas 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. |
Índice
Preface | 1 |
The Characteristic Polynomial | 19 |
Formal Power Series and Generating Functions | 37 |
Walk Generating Functions | 51 |
Quotients of Graphs | 76 |
Matchings and Walks | 98 |
Pfaffians | 113 |
Orthogonal Polynomials | 131 |
DistanceRegular Graphs | 195 |
Association Schemes | 221 |
Representations of DistanceRegular Graphs | 261 |
Polynomial Spaces | 285 |
QPolynomial Spaces | 307 |
Tight Designs | 333 |
Terminology | 353 |
359 | |
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Términos y frases comunes
adjacency matrix algebraic antipodal association scheme automorphism b₁ bipartite graph blocks C₁ cells Chapter characteristic polynomial closed walks coefficients combinatorial completely regular contains Corollary cycle deduce defined Delsarte denote determine distance-regular graph edges eigenvalue eigenvalue of G eigenvector elements equal equitable partition Exercise exponential generating function finite follows formal power series graph G graph of diameter Hence i-th idempotents identity ij-entry implies imprimitive inner product isomorphic k-subsets Lemma Let G linear combination matchings polynomial Math multiplicity non-trivial non-zero number of perfect number of vertices obtained orthogonal polynomials perfect codes perfect matchings permutation points Pol(N Pol(n,r polynomial of degree Proof prove Q-polynomial result rows Schur Section sequence of orthogonal Show span spherical polynomial space strongly regular graph subset subspace Suppose t-design Theorem theory unit sphere valency vector space vertex set vertices of G walks of length weighted zero
Pasajes populares
Página 331 - P. Delsarte, Four fundamental parameters of a code and their combinatorial significance, Info.
Página 331 - P. Delsarte, J.-M. Goethals and JJ Seidel, Spherical codes and designs, Geom. Dedicata 6 (1977) 363-388.
Referencias a este libro
Graph Symmetry: Algebraic Methods and Applications Gena Hahn,Gert Sabidussi Vista previa restringida - 1997 |