Combinatorics: Topics, Techniques, Algorithms
Combinatorics is a subject of increasing importance because of its links with computer science, statistics, and algebra. This textbook stresses common techniques (such as generating functions and recursive construction) that underlie the great variety of subject matter, and the fact that a constructive or algorithmic proof is more valuable than an existence proof. The author emphasizes techniques as well as topics and includes many algorithms described in simple terms. The text should provide essential background for students in all parts of discrete mathematics.
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algebra algorithm argument automorphism group axioms bijection binary binomial coefficients bipartite blocks bound calculate cardinality Chapter choices codewords colours column combinatorics construction contains corresponding coset counting cycle index defined digraph disjoint distinct edges elements entries equal equation equivalence classes example Exercise exists exponential fact follows formula function geometry given gives graph Hadamard Hadamard matrix Hamiltonian circuit induced subgraph induction infinite isomorphic Latin squares lattice Lemma length Let G linear linear code matrix matroid Moore graph multiplication n-set natural numbers non-zero orbits ordinal numbers orthogonal pairs partition path permutation group points polynomial poset positive integer problem projective plane proof Proposition Prove Ramsey's Theorem real numbers recurrence relation result satisfies Section sequence space Steiner triple system subgraph subsets subspaces Suppose symmetric theory triangle unique valency values vector vertex set vertices words zero