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ruskey f combinatorial generation 2003

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Textbook in PDF format Humanity has long enjoyed making lists. All children delight in their new-found ability to count 1,2,3, etc., and it is a profound revelation that this process can be carried out indefinitely. The fascination of finding the next unknown prime or of listing the digits of π appeals to the general population, not just mathematicians. The desire to produce lists almost seems to be an innate part of our nature. Furthermore, the solution to many problems begins by listing the possibilities that can arise. There are lists of mathematical objects that have a historical interest, or maybe I should say that there are lists of historical objects that have a mathematical interest. Examples include the Fu Hsi sequencing of the hexagrams of the I Ching (e.g., as described in Martin Gardner - Knotted Donuts) and the Murasaki diagrams of the Tale of the Genji (by Lady Shikibu Murasaki, 1000 A.D.) as explained in Gould. Viewed properly, these are lists of the first 64 binary numbers 0, 1... 63 and all 52 partitions of a 5-set, respectively. They are illustrated in Figures 1 and 2 at the end of this preface. However, it was not until the advent of the digital computer that the construction of long lists of combinatorial objects became a non-tedious exercise. Indeed, some of the first applications of computers were for producing such lists. With the computer as our able assistant we can construct interesting lists to our hearts content. There is deeply satisfying feeling that one obtains by watching a well ordered list of combinatorial objects marching down the computer screen. The author hopes that the readers of this book will implement some of the algorithms found herein and experience this feeling for themselves! These lists are not only interesting but can be extremely useful. Nearly every computer scientist and mathematician has encountered some instance where they solved a problem simply by listing all the possibilities and checking for a desired property. One can find applications of the ideas in this book to circuit design, statistical computing, chemistry, and operations research, just to name a few

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