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Advanced combinatorics - Comtet L.

 
Название: Advanced combinatorics
Автор: Comtet L.
Категория: Математика
Тип: Книга
Дата: 30.12.2008 15:31:03
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Описание: Notwithstanding its title, the reader will not find in this book a systematic account of this huge subject. Certain classical aspects have been passed by, and the true title ought to be "Various questions of elementary combinatorial analysis". For instance, we only touch upon the subject of graphs and configurations, but there exists a very extensive and good literature on this subject. For this we refer the reader to the bibliography at the end ofthevoiume. The true beginnings of combinatorial analysis (also called combinatory analysis) coincide with the beginnings of probability theory in the 17th century. For about two centuries it vanished as an autonomous subject. But the advance of statistics, with an ever-increasing demand for configurations as well as the advent and development of computers, have, beyond doubt, contributed to reinstating this subject after such a long period of negligence. For a long time the aim of combinatorial analysis was to count the different ways of arranging objects under given circumstances. Hence, many of the traditional problems of analysis or geometry which are con- СбГПби at a Certain moment Witu liFlite Structures, ixaVC a CGliiuinaiGriai character. Today, combinatorial analysis is also relevant to problems of existence, estimation and structuration, like all other parts of mathematics, but exclusively {отfinite sets. My idea is here to take the uninitiated reader along a path strewn with particular problems, and I can very well amagine that this journey may jolt a student who is used to easy generalizations, especially when only some of the questions I treat can be extended at all, and difficult or unsolved extensions at that, too. Meanwhile, the treatise remains firmly elementary and almost no mathematics of advanced college level will be necessary. At the end of each chapter I provide statements in the form of exercises that serve as supplementary material, and I have indicated with a star those that seem most difficult. In this respect, I have attempted to write down
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