## Combinatorics: Ancient & ModernWho first presented Pascal's triangle? (It was not Pascal.) Who first presented Hamiltonian graphs? (It was not Hamilton.) Who first presented Steiner triple systems? (It was not Steiner.) The history of mathematics is a well-studied and vibrant area of research, with books and scholarly articles published on various aspects of the subject. Yet, the history of combinatorics seems to have been largely overlooked. This book goes some way to redress this and serves two main purposes: 1) it constitutes the first book-length survey of the history of combinatorics; and 2) it assembles, for the first time in a single source, researches on the history of combinatorics that would otherwise be inaccessible to the general reader. Individual chapters have been contributed by sixteen experts. The book opens with an introduction by Donald E. Knuth to two thousand years of combinatorics. This is followed by seven chapters on early combinatorics, leading from Indian and Chinese writings on permutations to late-Renaissance publications on the arithmetical triangle. The next seven chapters trace the subsequent story, from Euler's contributions to such wide-ranging topics as partitions, polyhedra, and latin squares to the 20th century advances in combinatorial set theory, enumeration, and graph theory. The book concludes with some combinatorial reflections by the distinguished combinatorialist, Peter J. Cameron. This book is not expected to be read from cover to cover, although it can be. Rather, it aims to serve as a valuable resource to a variety of audiences. Combinatorialists with little or no knowledge about the development of their subject will find the historical treatment stimulating. A historian of mathematics will view its assorted surveys as an encouragement for further research in combinatorics. The more general reader will discover an introduction to a fascinating and too little known subject that continues to stimulate and inspire the work of scholars today. |

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### Vsebina

Indian combinatorics | |

China | |

Jewish combinatorics | |

Renaissance combinatorics | |

The arithmetical triangle | |

Early graph theory | |

Partitions | |

Latin squares | |

Enumeration 18th20th centuries | |

Combinatorial set theory | |

Modern graph theory | |

A personal view of combinatorics | |

Notes on contributors | |

Picture sources and acknowledgements | |

### Druge izdaje - Prikaži vse

Combinatorics: Ancient & Modern Robin Wilson,Senior Lecturer Faculty of Mathematics Robin Wilson,John J. Watkins Predogled ni na voljo - 2015 |

### Pogosti izrazi in povedi

Abraham de Moivre algebraic algorithms Amer appeared arithmetical triangle arrangements Bernoulli binary calculated Cardano Cayley century Chapter coefficients colours column combinatorial problems configurations Conjectandi conjecture construction contains corresponding diagram dice digits edges elements enumeration Erdős Euler example figurate numbers finite formula four fourcolour G. H. Hardy geometry given number graph theory Ibn Munʿim integers J. J. Sylvester Jacob Bernoulli Kircher Kirkman Kitāb later Leibniz letters Li Shanlan magic squares Math Mathematical Society mathematician Mersenne method Moivre Montmort multiply Nārāyaṇa number of combinations number of permutations number theory obtained orthogonal latin squares pair paper Pascal pentagonal number theorem polynomial possible prastāra projective plane proof proved published Redfield repetition result rule Sciences sequence solution solved square of order Steiner triple system subsets sudoku syllables Sylvester symbols theorem total number transversals treatise triple system variations vertex vertices wrote