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Complexity: Knots, Colourings and Countings
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These notes are based on a series of lectures given at the Advanced Research Institute of Discrete Applied Mathematics held at Rutgers University. Their aim is to link together algorithmic problems arising in knot theory, statistical physics and classical combinatorics. Apart from the theory of computational complexity concerned with enumeration problems, introductions are given to several of the topics treated, such as combinatorial knot theory, randomised approximation algorithms, percolation and random cluster models. To researchers in discrete mathematics, computer science and statistical physics, this book will be of great interest, but any non-expert should find it an appealing guide to a very active area of research.


"...suitable for advanced graduate students and researchers in complexity theory...The list of references is long and good, and the index is useful." Computing Reviews

" urbane presentation...of the seemingly disparate threads that will some day be the new math...the author has attained a degree of clarity and readability that few mathematicians today are capable of." Gian-Carlo Rota

"...certain to be a valuable reference..." Lorenzo Traldi, Mathematical Reviews

"A clear and up-to-date survey of what's known--and what's still unknown." American Mathematical Monthly

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