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  1. Complexity
    knots, colourings, and counting
    Published: 1993
    Publisher:  Cambridge University Press, Cambridge

    1. The complexity of enumeration -- 1.1. Basics of complexity -- 1.2. Counting problems -- 1.3. # P-complete problems -- 1.4. Decision easy, counting hard -- 1.5. The Permanent -- 1.6. Hard enumeration problems not thought to be # P-complete -- 1.7.... more

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    1. The complexity of enumeration -- 1.1. Basics of complexity -- 1.2. Counting problems -- 1.3. # P-complete problems -- 1.4. Decision easy, counting hard -- 1.5. The Permanent -- 1.6. Hard enumeration problems not thought to be # P-complete -- 1.7. Self-avoiding walks -- 1.8. Toda's theorems -- 2. Knots and links -- 2.2. Tait colourings -- 2.3. Classifying knots -- 2.4. Braids and the braid group -- 2.5. The braid index and the Seifert graph of a link -- 2.6. Enzyme action -- 2.7. The number of knots and links -- 2.8. The topology of polymers -- 3. Colourings, flows and polynomials -- 3.1. The chromatic polynomial -- 3.2. The Whitney-Tutte polynomials -- 3.3. Tutte Grothendieck invariants -- 3.4. Reliability theory -- 3.5. Flows over an Abelian group -- 3.6. Ice models -- 3.7. A catalogue of invariants -- 4. Statistical physics -- 4.1. Percolation processes -- 4.2. The Ising model -- 4.3. Combinatorial interpretations -- 4.4. The Ashkin-Teller-Potts model -- 4.5. The random cluster model -- 4.6. Percolation in the random cluster model -- 5. Link polynomials and the Tait conjectures -- 5.1. The Alexander polynomial -- 5.2. The Jones polynomial and Kauffman bracket -- 5.3. The Homfly polynomial -- 5.4. The Kauffman 2-variable polynomial -- 5.5. The Tait conjectures -- 5.6. Thistlethwaite's nontriviality criterion -- 5.7. Link invariants and statistical mechanics -- 6. Complexity questions -- 6.1. Computations in knot theory -- 6.2. The complexity of the Tutte plane -- 6.3. The complexity of knot polynomials -- 6.4. The complexity of the Ising model -- 6.5. Reliability and other computations -- 7. The complexity of uniqueness and parity -- 7.1. Unique solutions -- 7.2. Unambiguous machines and one-way functions -- 7.3. The Valiant-Vazirani theorem -- 7.4. Hard counting problems not parsimonious with SAT -- 7.5. The curiosity of parity -- 7.6. Toda's theorem on parity -- 8. Approximation and randomisation -- 8.1. Metropolis methods -- 8.2. Approximating to within a ratio -- 8.3. Generating solutions at random -- 8.4. Rapidly mixing Markov chains -- 8.5. Computing the volume of a convex body -- 8.6. Approximations and the Ising model. 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

     
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    Source: Union catalogues
    Language: English
    Media type: Ebook
    Format: Online
    ISBN: 9781107088696; 1107088690; 9780511752506; 0511752504
    Other identifier:
    9780521457408
    Series: London mathematical society lecture note series ; 186
    Subjects: Computational complexity; Knot theory; Combinatorial analysis; Statistical physics; Computational complexity; Knot theory; Combinatorial analysis; Statistical physics; complexite; MATHEMATICS ; Infinity; MATHEMATICS ; Logic; Combinatorial analysis; Computational complexity; Knot theory; Statistical physics; Komplexitätstheorie; Graphentheorie; Knopentheorie; Complexiteit; Complexité de calcul (Informatique); Noeud, théorie du; Lien, théorie du
    Scope: Online Ressource (viii, 163 p.), ill.
    Notes:

    Includes bibliographical references (p. 143-159) and index. - Description based on print version record
  2. Symbolismus und symbolische Logik
    die Idee der Ars Combinatoria in der Entwicklung der modernen Dichtung
    Author: Neubauer, John
    Published: 1978
    Publisher:  Fink, München

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    Source: Union catalogues
    Language: German
    Media type: Ebook
    Format: Online
    ISBN: 3770515811
    Other identifier:
    RVK Categories: EC 2490 ; EC 3000 ; GM 1712
    Series: Humanistische Bibliothek ; 28
    Subjects: Combinatorial analysis; Logic, Symbolic and mathematical; Mathematics and literature; Literatur; Poetik; Imagination; Naturwissenschaften; Kombinatorik
    Scope: 236 S., Ill.
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    Volltext // 2009 digitalisiert von: Bayerische Staatsbibliothek, München. Exemplar der Bayerischen Staatsbibliothek mit der Signatur: Z 69.1039,I-27/28#28