Combinatorics: Topics, Techniques, Algorithms
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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algorithm apply argument assume blocks bound calculate called Chapter choices choose closed coefficients colours column combinatorics condition connected consider consists construction contains corresponding counting cycle defined definition distinct edges elements entries equal equation equivalence example Exercise exists expression fact field finite fixed follows formula function geometry given gives graph holds important induction infinite integer Latin squares lattice least length lies linear matrix multiplication natural Note objects obtain pairs partial partition path permutation plane points polynomial poset positive possible problem projective PROOF Proposition Prove question recurrence relation represented respectively result satisfies sequence solution space step structure subsets Suppose symmetric Theorem theory triple system true unique valency values vector vertex vertices zero