Verfügbarkeit: Complexity | Technische Universität München

Complexity: knots, colourings and counting

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Bibliographische Detailangaben
Beteilige Person:	Welsh, Dominic J. A. (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Cambridge u.a. Cambridge Univ. Press 1993
Ausgabe:	1. publ.
Schriftenreihe:	London Mathematical Society: London Mathematical Society lecture note series 186
Schlagwörter:	Kombinatorik Knotentheorie Abzählen Komplexität Statistische Physik Enumeration Knoten > Mathematik
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005446041&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	VIII, 163 S. graph. Darst.
ISBN:	0521457408

Internformat

MARC


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Datensatz im Suchindex

_version_	1819311528556363776
adam_text	Contents 1 The complexity of enumeration 1 1.1 Basics of complexity 1 1.2 Counting problems 3 1.3 # P-complete problems 6 1.4 Decision easy, counting hard 10 1.5 The Permanent 11 1.6 Hard enumeration problems not thought to be #P-complete. 14 1.7 Self-avoiding walks 16 1.8 Toda s theorems 17 1.9 Additional notes 19 2 Knots and links 20 2.1 Introduction 20 2.2 Tait colourings 23 2.3 Classifying knots 25 2.4 Braids and the braid group 29 2.5 The braid index and the Seifert graph of a link 31 2.6 Enzyme action 35 2.7 The number of knots and links 37 2.8 The topology of polymers 37 2.9 Additional notes 40 3 Colourings, flows and polynomials 42 3.1 The chromatic polynomial 42 3.2 The Whitney-Tutte polynomials 44 3.3 Tutte Grothendieck invariants 46 3.4 Reliability theory 48 3.5 Flows over an Abelian group 49 3.6 Ice models 50 3.7 A catalogue of invariants 51 3.8 Additional notes 53 4 Statistical physics 54 4.1 Percolation processes 54 4.2 The Ising model 58 4.3 Combinatorial interpretations 60 v vi Contents 4.4 The Ashkin-Teller-Potts model 62 4.5 The random cluster model 64 4.6 Percolation in the random cluster model 67 4.7 Additional notes 70 5 Link polynomials and the Tait conjectures 71 5.1 The Alexander polynomial 71 5.2 The Jones polynomial and Kauffman bracket 75 5.3 The Homfly polynomial 82 5.4 The Kauffman 2-variable polynomial 84 5.5 The Tait conjectures 87 5.6 Thistlethwaite s nontriviality criterion 90 5.7 Link invariants and statistical mechanics 92 5.8 Additional notes 94 6 Complexity questions 95 6.1 Computations in knot theory 95 6.2 The complexity of the Tutte plane 96 6.3 The complexity of knot polynomials 100 6.4 The complexity of the Ising model 104 6.5 Reliability and other computations 107 6.6 Additional notes 109 7 The complexity of uniqueness and parity 110 7.1 Unique solutions 110 7.2 Unambiguous machines and one-way functions . 113 7.3 The Valiant-Vazirani theorem 114 7.4 Hard counting problems not parsimonious with SAT 117 7.5 The curiosity of parity 118 7.6 Toda s theorem on parity 122 7.7 Additional notes 123 8 Approximation and randomisation 124 8.1 Metropolis methods 124 8.2 Approximating to within a ratio 126 8.3 Generating solutions at random 129 8.4 Rapidly mixing Markov chains 130 8.5 Computing the volume of a convex body 132 8.6 Approximations and the Ising model 135 8.7 Some open questions 137 8.8 Additional notes 141 References 143
any_adam_object	1
author	Welsh, Dominic J. A.
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illustrated	Illustrated
indexdate	2024-12-20T09:19:04Z
institution	BVB
isbn	0521457408
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-005446041
oclc_num	246644008
open_access_boolean
owner	DE-355 DE-BY-UBR DE-384 DE-12 DE-739 DE-29T DE-20 DE-703 DE-19 DE-BY-UBM DE-11 DE-83 DE-188
owner_facet	DE-355 DE-BY-UBR DE-384 DE-12 DE-739 DE-29T DE-20 DE-703 DE-19 DE-BY-UBM DE-11 DE-83 DE-188
physical	VIII, 163 S. graph. Darst.
publishDate	1993
publishDateSearch	1993
publishDateSort	1993
publisher	Cambridge Univ. Press
record_format	marc
series	London Mathematical Society: London Mathematical Society lecture note series
series2	London Mathematical Society: London Mathematical Society lecture note series
spellingShingle	Welsh, Dominic J. A. Complexity knots, colourings and counting London Mathematical Society: London Mathematical Society lecture note series Kombinatorik (DE-588)4031824-2 gnd Knotentheorie (DE-588)4164318-5 gnd Abzählen (DE-588)4508960-7 gnd Komplexität (DE-588)4135369-9 gnd Statistische Physik (DE-588)4057000-9 gnd Enumeration (DE-588)4242271-1 gnd Knoten Mathematik (DE-588)4164314-8 gnd
subject_GND	(DE-588)4031824-2 (DE-588)4164318-5 (DE-588)4508960-7 (DE-588)4135369-9 (DE-588)4057000-9 (DE-588)4242271-1 (DE-588)4164314-8
title	Complexity knots, colourings and counting
title_auth	Complexity knots, colourings and counting
title_exact_search	Complexity knots, colourings and counting
title_full	Complexity knots, colourings and counting D. J. A. Welsh
title_fullStr	Complexity knots, colourings and counting D. J. A. Welsh
title_full_unstemmed	Complexity knots, colourings and counting D. J. A. Welsh
title_short	Complexity
title_sort	complexity knots colourings and counting
title_sub	knots, colourings and counting
topic	Kombinatorik (DE-588)4031824-2 gnd Knotentheorie (DE-588)4164318-5 gnd Abzählen (DE-588)4508960-7 gnd Komplexität (DE-588)4135369-9 gnd Statistische Physik (DE-588)4057000-9 gnd Enumeration (DE-588)4242271-1 gnd Knoten Mathematik (DE-588)4164314-8 gnd
topic_facet	Kombinatorik Knotentheorie Abzählen Komplexität Statistische Physik Enumeration Knoten Mathematik
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005446041&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000000130
work_keys_str_mv	AT welshdominicja complexityknotscolouringsandcounting

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