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Preface to the first edition | |

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Preface to the second edition | |

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Graphs | |

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Terminology of graphs and digraphs | |

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Eulerian circuits | |

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Hamiltonian circuits | |

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Trees | |

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Cayley's theorem | |

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Spanning trees and the greedy algorithm | |

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Search trees | |

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Strong connectivity | |

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Colorings of graphs and Ramsey's theorem | |

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Brooks' theorem | |

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Ramsey's theorem and Ramsey numbers | |

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The Lovasz sieve | |

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The Erdos-Szekeres theorem | |

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Turan's theorem and extremal graphs | |

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Turan's theorem and extremal graph theory | |

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Systems of distinct representatives | |

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Bipartite graphs | |

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P. Hall's condition | |

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SDRs | |

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Konig's theorem | |

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Birkhoff's theorem | |

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Dilworth's theorem and extremal set theory | |

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Partially ordered sets | |

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Dilworth's theorem | |

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Sperner's theorem | |

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Symmetric chains | |

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The Erdos-Ko-Rado theorem | |

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Flows in networks | |

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The Ford-Fulkerson theorem | |

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The integrality theorem | |

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A generalization of Birkhoff's theorem | |

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Circulations | |

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De Bruijn sequences | |

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The number of De Bruijn sequences | |

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Two (0, 1 *) problems: addressing for graphs and a hash-coding scheme | |

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Quadratic forms | |

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Winkler's theorem | |

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Associative block designs | |

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The principle of inclusion and exclusion; inversion formulae | |

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Inclusion-exclusion | |

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Derangements | |

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Euler indicator | |

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Mobius function | |

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Mobius inversion | |

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Burnside's lemma | |

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Probleme des menages | |

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Permanents | |

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Bounds on permanents | |

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Schrijver's proof of the Minc conjecture | |

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Fekete's lemma | |

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Permanents of doubly stochastic matrices | |

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The Van der Waerden conjecture | |

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The early results of Marcus and Newman | |

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London's theorem | |

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Egoritsjev's proof | |

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Elementary counting; Stirling numbers | |

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Stirling numbers of the first and second kind | |

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Bell numbers | |

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Generating functions | |

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Recursions and generating functions | |

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Elementary recurrences | |

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Catalan numbers | |

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Counting of trees | |

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Joyal theory | |

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Lagrange inversion | |

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Partitions | |

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The function P[subscript k] (n) | |

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The partition function | |

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Ferrers diagrams | |

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Euler's identity | |

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Asymptotics | |

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The Jacobi triple product identity | |

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Young tableaux and the hook formula | |

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(0, 1)-Matrices | |

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Matrices with given line sums | |

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Counting (0, 1)-matrices | |

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Latin squares | |

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Orthogonal arrays | |

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Conjugates and isomorphism | |

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Partial and incomplete Latin squares | |

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Counting Latin squares | |

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The Evans conjecture | |

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The Dinitz conjecture | |

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Hadamard matrices, Reed--Muller codes | |

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Hadamard matrices and conference matrices | |

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Recursive constructions | |

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Paley matrices | |

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Williamson's method | |

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Excess of a Hadamard matrix | |

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First order Reed-Muller codes | |

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Designs | |

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The Erdos-De Bruijn theorem | |

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Steiner systems | |

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Balanced incomplete block designs | |

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Hadamard designs | |

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Counting | |

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(higher) incidence matrices | |

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The Wilson--Petrenjuk theorem | |

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Symmetric designs | |

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Projective planes | |

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Derived and residual designs | |

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The Bruck--Ryser--Chowla theorem | |

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Constructions of Steiner triple systems | |

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Write-once memories | |

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Codes and designs | |

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Terminology of coding theory | |

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The Hamming bound | |

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The Singleton bound | |

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Weight enumerators and MacWilliams' theorem | |

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The Assmus--Mattson theorem | |

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Symmetry codes | |

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The Golay codes | |

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Codes from projective planes | |

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Strongly regular graphs and partial geometries | |

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The Bose--Mesner algebra | |

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Eigenvalues | |

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The integrality condition | |

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Quasisymmetric designs | |

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The Krein condition | |

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The absolute bound | |

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Uniqueness theorems | |

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Partial geometries | |

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Examples | |

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Directed strongly regular graphs | |

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Neighborhood regular graphs | |

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Orthogonal Latin squares | |

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Pairwise orthogonal Latin squares and nets | |

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Euler's conjecture | |

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The Bose--Parker--Shrikhande theorem | |

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Asymptotic existence | |

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Orthogonal arrays and transversal designs | |

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Difference methods | |

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Orthogonal subsquares | |

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Projective and combinatorial geometries | |

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Projective and affine geometries | |

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Duality | |

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Pasch's axiom | |

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Desargues' theorem | |

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Combinatorial geometries | |

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Geometric lattices | |

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Greene's theorem | |

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Gaussian numbers and q-analogues | |

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Chains in the lattice of subspaces | |

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q-analogue of Sperner's theorem | |

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Interpretation of the coefficients of the Gaussian polynomials | |

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Spreads | |

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Lattices and Mobius inversion | |

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The incidence algebra of a poset | |

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The Mobius function | |

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Chromatic polynomial of a graph | |

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Weisner's theorem | |

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Complementing permutations of geometric lattices | |

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Connected labeled graphs | |

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MDS codes | |

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Combinatorial designs and projective geometries | |

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Arcs and subplanes in projective planes | |

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Blocking sets | |

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Quadratic and Hermitian forms | |

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Unitals | |

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Generalized quadrangles | |

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Mobius planes | |

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Difference sets and automorphisms | |

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Block's lemma | |

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Automorphisms of symmetric designs | |

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Paley--Todd and Stanton--Sprott difference sets | |

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Singer's theorem | |

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Difference sets and the group ring | |

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The Multiplier Theorem and extensions | |

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Homomorphisms and further necessary conditions | |

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Codes and symmetric designs | |

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The sequence of codes of a symmetric design | |

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Wilbrink's theorem | |

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Association schemes | |

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Examples | |

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The eigenmatrices and orthogonality relations | |

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Formal duality | |

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The distribution vector of a subset | |

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Delsarte's inequalities | |

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Polynomial schemes | |

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Perfect codes and tight designs | |

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(More) algebraic techniques in graph theory | |

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Tournaments and the Graham--Pollak theorem | |

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The spectrum of a graph | |

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Hoffman's theorem | |

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Shannon capacity | |

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Applications of interlacing and Perron--Frobenius | |

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Graph connectivity | |

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Vertex connectivity | |

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Menger's theorem | |

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Tutte connectivity | |

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Planarity and coloring | |

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The chromatic polynomial | |

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Kuratowski's theorem | |

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Euler's formula | |

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The Five Color Theorem | |

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List-colorings | |

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Whitney Duality | |

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Whitney duality | |

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Circuits and cutsets | |

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MacLane's theorem | |

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Embeddings of graphs on surfaces | |

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Embeddings on arbitrary surfaces | |

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The Ringel--Youngs theorem | |

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The Heawood conjecture | |

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The Edmonds embedding technique | |

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Electrical networks and squared squares | |

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The matrix-tree theorem | |

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De Bruijn sequences | |

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The network of a squared rectangle | |

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Kirchhoff's theorem | |

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Polya theory of counting | |

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The cycle index of a permutation group | |

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Counting orbits | |

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Weights | |

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Necklaces | |

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The symmetric group | |

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Stirling numbers | |

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Baranyai's theorem | |

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One-factorizations of complete graphs and complete designs | |

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Hints and comments on problems | |

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Hints | |

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Suggestions | |

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Comments on the problems in each chapter | |

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Formal power series | |

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Formal power series ring | |

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Formal derivatives | |

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Inverse functions | |

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Residues | |

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The Lagrange--Burmann formula | |

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Name Index | |

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Subject Index | |