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Combinatorial Designs and Tournaments (Oxford Lecture Series in Mathematics and Its Applications) [Hardcover]

Ian Anderson

Price: 101.00 & FREE Delivery in the UK. Details
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Book Description

10 April 1997 0198500297 978-0198500292
published by Ellis Horwood in 1990 and out of print for several years. It is not a second edition.

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This is an extensively revised version of the very successfulCombinatorial Designs: Construction Methods which was published in 1990 by Ellis Horwood and is now out of print. A new chapter on league schedules is now included, dealing with round robin tournaments, venue sequences, and carry over effects. Balanced tournament designs, double schedules, and bridge tournament designs are also covered, and there is some material on whist tournaments. The presentation is clear and reable. Throughout, the historical development of the material is emphasized. There are plenty of examples and exercises giving detailed constructions, and a copious bibliography is provided. The author is internationally respected as an expositor, and this book provides an excellent text and reference book for researchers.

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The modern study of block designs is often said to have begun with the publication in 1936 of a paper by the statistician F. Yates. Read the first page
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1 of 1 people found the following review helpful
5.0 out of 5 stars The mathematics of constructing a tournament schedule, the structure is theorem/proof 5 July 2010
By Charles Ashbacher - Published on Amazon.com
Creating the schedule for a tournament when there are restrictive factors is a complex task that cannot always be solved. The final chapter of the book deals with a whist or doubles tennis tournament and the restrictions are as follows:

*) Each player plays in one game per round
*) Each player partners with every other player exactly one time
*) Each player opposes every other player exactly two times

The family of solutions is presented in the form of theorems that are stated and then proven and they are based on the foundation presented in the previous chapters. Latin squares are the fundamental mathematical tool used throughout the book as they are an excellent way to represent a set of selections, which is of course what a schedule is.
This is a book for sophisticated mathematicians; the tactic used throughout is that of formal mathematics:

1) Background definitions
2) Statement of theorems
3) Detailed proof of theorem

The notation is somewhat unusual and can be a bit difficult to understand at times. A large set of exercises is given at the ends of the chapters although no solutions are included.
Creating a viable tournament from the massive number of possible combinations can only be done by using a combinatorial filter that will allow you to select the appropriate items that together form a solution. In this book, Anderson presents and proves those filters.
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