## Combinatorial Methods in Discrete MathematicsDiscrete mathematics is an important tool for the investigation of various models of functioning of technical devices, especially in the field of cybernetics. Here the author presents some complex problems of discrete mathematics in a simple and unified form using an original, general combinatorial scheme. Professor Sachkov's aim is to focus attention on results that illustrate the methods described. A distinctive aspect of the book is the large number of asymptotic formulae derived. Professor Sachkov begins with a discussion of block designs and Latin squares before proceeding to treat transversals, devoting much attention to enumerative problems. The main role in these problems is played by generating functions, considered in Chapter 4. The general combinatorial scheme is then introduced and in the last chapter Polya's enumerative theory is discussed. This is an important book for graduate students and professionals that describes many ideas not previously available in English; the author has updated the text and references where appropriate. |

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### Contents

1 Combinatorial configurations | 1 |

2 Transversals and permanents | 49 |

3 Generating functions | 102 |

4 Graphs and mappings | 165 |

5 The general combinatorial scheme | 209 |

6 Polyas theorem and its applications | 272 |

295 | |

303 | |

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### Common terms and phrases

acting addition allocations Applying assume asymmetric n-basis asymptotic blocks called cells classes clear columns combinatorial commutative complete components composition condition conﬁgurations connected consider consists construct containing corresponding covering cycle deﬁned denote derive determined distinct edges elements enumerator equality equation equivalence classes estimate exactly exists ﬁnd ﬁnite ﬁrst ﬁxed formula function given graph Hence it follows holds identity implies independent inequality integral introduce inverse labeled Latin squares Lemma length linear m-samples mapping matrix means method multiplication Note obtain operation orthogonal pairs particles particular partitions permutation polynomials positive problem Proof properties proved relation represented respect result rooted satisfy sequence sides speciﬁcation subsets substitution summands symmetric theorem theory transformation trees unique unit valid values variables vector vertices weight zero