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Complexity: Knots, Colourings and Countings

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Complexity: Knots, Colourings and Countings

Complexity: Knots, Colourings and Countings

Dominic Welsh, University of Oxford
July 2013
Adobe eBook Reader
9781107108547
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    Description

    The aim of these notes is to link algorithmic problems arising in knot theory with statistical physics and classical combinatorics. Apart from the theory of computational complexity needed to deal with enumeration problems, introductions are given to several of the topics, such as combinatorial knot theory, randomized approximation models, percolation, and random cluster models.

    Reviews & endorsements

    "...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

    "...an 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

    See more reviews

    Product details

    July 2013
    Adobe eBook Reader
    9781107108547
    0 pages
    0kg
    70 line figures
    This ISBN is for an eBook version which is distributed on our behalf by a third party.

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    Contents

    Table of Contents

    • 1. The complexity of enumeration
    • 2. Knots and links
    • 3. Colourings, flows and polynomials
    • 4. Statistical physics
    • 5. Link polynomials
    • 6. Complexity questions
    • 7. The complexity of uniqueness and parity
    • 8. Approximation and randomisation
    • References.
      • Show more
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