Algebraic combinatorics /
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| Author / Creator: | Godsil, C. D. (Christopher David), 1949- |
|---|---|
| Imprint: | New York : Chapman & Hall, 1993. |
| Description: | xv, 362 p. : ill. ; 24 cm. |
| Language: | English |
| Series: | Chapman and Hall mathematics Chapman & Hall mathematics. |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/2367013 |
Table of Contents:
- 1. The Matchings Polynomial. 1.1. Recurrences. 1.2. Integrals. 1.3. Rook Polynomials. 1.4. The Hit Polynomial. 1.5. Stirling and Euler Numbers. 1.6. Hit Polynomials and Integrals
- 2. The Characteristic Polynomial. 2.1. Coefficients and Recurrences. 2.2. Walks and the Characteristic Polynomial. 2.3. Eigenvectors. 2.4. Regular Graphs. 2.5. The Spectral Decomposition. 2.6. Some Further Matrix Theory
- 3. Formal Power Series and Generating Functions. 3.1. Formal Power Series. 3.2. Limits. 3.3. Operations on Power Series. 3.4. Exp and Log. 3.5. Non-linear Equations. 3.6. Applications and Examples
- 4. Walk Generating Functions. 4.1. Jacobi's Theorem. 4.2. Walks and Paths. 4.3. A Decomposition Formula. 4.4. The Christoffel-Darboux Identity. 4.5. Vertex Reconstruction. 4.6. Cospectral Graphs. 4.7. Random Walks on Graphs
- 5. Quotients of Graphs. 5.1. Equitable Partitions. 5.2. Eigenvalues and Eigenvectors. 5.3. Walk-Regular Graphs. 5.4. Generalised Interlacing. 5.5. Covers. 5.6. The Spectral Radius of a Tree
- 6. Matchings and Walks. 6.1. The Path-Tree. 6.2. Tree-Like Walks. 6.3. Consequences of Reality. 6.4. Christoffel-Darboux Identities
- 7. Pfaffians. 7.1. The Pfaffian of a Skew Symmetric Matrix. 7.2. Pfaffians and Determinants. 7.3. Row Expansions. 7.4. Oriented Graphs. 7.5. Orientations. 7.6. The Difficulty of Counting Perfect Matchings
- 8. Orthogonal Polynomials. 8.1. The Definitions. 8.2. The Three-Term Recurrence. 8.3. The Christoffel-Darboux Formula. 8.4. Discrete Orthogonality. 8.5. Sturm Sequences
- 9. Moment Sequences. 9.1. Moments and Walks. 9.2. Moment Generating Functions. 9.3. Hermite and Laguerre Polynomials. 9.4. The Chebyshev Polynomials. 9.5. The Charlier Polynomials. 9.6. Sheffer Sequences of Polynomials. 9.7. Characterising Polynomials of Meixner Type. 9.8. The Polynomials of Meixner Type
- 10. Strongly Regular Graphs. 10.1. Basic Theory. 10.2. Conference Graphs. 10.3. Designs. 10.4. Orthogonal Arrays
- 11. Distance-Regular Graphs. 11.1. Some Families. 11.2. Distance Matrices. 11.3. Parameters. 11.4. Quotients. 11.5. Imprimitive Distance-Regular Graphs. 11.6. Codes. 11.7. Completely Regular Subsets
- 12. Association Schemes. 12.1. Generously Transitive Permutation Groups. 12.2. p's and q's. 12.3. P- and Q-Polynomial Association Schemes. 12.4. Products. 12.5. Primitivity and Imprimitivity. 12.6. Codes and Anticodes. 12.7. Equitable Partitions of Matrices. 12.8. Characters of Abelian Groups. 12.9. Cayley Graphs. 12.10. Translation Schemes and Duality
- 13. Representations of Distance-Regular Graphs. 13.1. Representations of Graphs. 13.2. The Sequence of Cosines. 13.3. Injectivity. 13.4. Eigenvalue Multiplicities. 13.5. Bounding the Diameter. 13.6. Spherical Designs. 13.7. Bounds for Cliques. 13.8. Feasible Automorphisms
- 14. Polynomial Spaces. 14.1. Functions. 14.2. The Axioms. 14.3. Examples. 14.4. The Degree of a Subset. 14.5. Designs. 14.6. The Johnson Scheme. 14.7. The Hamming Scheme. 14.8. Coding Theory. 14.9. Group-Invariant Designs. 14.10. Weighted Designs
- 15. Q-Polynomial Spaces. 15.1. Zonal Orthogonal Polynomials. 15.2. Zonal Orthogonal Polynomials: Examples. 15.3. The Addition Rule. 15.4. Spherical Polynomial Spaces. 15.5. Harmonic Polynomials. 15.6. Association Schemes. 15.7. Q-Polynomial Association Schemes. 15.8. Incidence Matrices for Subsets. 15.9. J(v,k) is Q-Polynomial
- 16. Tight Designs. 16.1. Tight Bounds. 16.2. Examples and Non-Examples. 16.3. The Grassman Space. 16.4. Linear Programming. 16.5. Bigger Bounds.