Combinatorics: Topics, Techniques, AlgorithmsCombinatorics 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 |
Common terms and phrases
a₁ algebra algorithm argument automorphism group axioms B₁ bijection binary binomial coefficients bipartite blocks bound cardinality Chapter codewords colours column combinatorics construction contains corresponding coset counting cycle index defined digraph disjoint edges elements entries equal equation equivalence classes example Exercise exists exponential fact follows formula function geometry given graph Hadamard matrix Hall's induction infinite intersecting isomorphic k-sets k-subsets Latin squares lattice Lemma length Let G linear linear code matrix matroid Möbius Möbius function Moore graph multiplication n-set n-tuple natural numbers non-zero orbits 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 vertices words zero