Combinatorics: Topics, Techniques, AlgorithmsCambridge University Press, 1994 M10 6 Combinatorics is a subject of increasing importance, owing to its links with computer science, statistics and algebra. This is a textbook aimed at second-year undergraduates to beginning graduates. It stresses common techniques (such as generating functions and recursive construction) which underlie the great variety of subject matter and also stresses the fact that a constructive or algorithmic proof is more valuable than an existence proof. The book is divided into two parts, the second at a higher level and with a wider range than the first. Historical notes are included which give a wider perspective on the subject. More advanced topics are given as projects and there are a number of exercises, some with solutions given. |
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Combinatorics: Topics, Techniques, Algorithms Peter J. Cameron,School of Mathematical Sciences Peter J Cameron No preview available - 1994 |
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algebra algorithm automorphism group axioms bijection binomial coefficients bipartite blocks bound canbe Chapter codewords colours column combinatorics construction contains corresponding coset counting cycle index defined disjoint edges elements entries equal equation Euler’s example Exercise exists exponential finite follows formula function geometry given graph Hadamard matrix Hall’s Hamiltonian circuit induced subgraph induction infinite intersecting inthe isomorphic ksubsets Latin squares lattice Lemma length linear matrix matroid Möbius Möbius function multiplication natural numbers nonzero nset ntuple numberof ofthe pairs partition permutation group points polynomial poset positive integers problem projective plane proof Proposition Prove Ramsey’s Theorem real numbers recurrence relation result ROOF satisfies Section sequence setof space Steiner triple system subgraph subsets subspaces Suppose symmetric thatthe thenumber theory triangle unique valency vector vertex vertices words zero