LinKnot: knot theory by computer
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Hackensack, NJ [u.a.]
World Scientific
c2007
|
| Schriftenreihe: | K & E series on knots and everything
21 |
| Schlagworte: | |
| Online-Zugang: | Table of contents only Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references (p. 459-474) and index |
| Beschreibung: | ix, 485 p. ill. 24 cm |
| ISBN: | 9789812772237 9812772235 |
Internformat
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| 245 | 1 | 0 | |a LinKnot |b knot theory by computer |c Slavik Jablan, Radmila Sazdanović |
| 264 | 1 | |a Hackensack, NJ [u.a.] |b World Scientific |c c2007 | |
| 300 | |a ix, 485 p. |b ill. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a K & E series on knots and everything |v 21 | |
| 500 | |a Includes bibliographical references (p. 459-474) and index | ||
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Knot theory |x Data processing | |
| 650 | 4 | |a Link theory |x Data processing | |
| 650 | 0 | 7 | |a Knotentheorie |0 (DE-588)4164318-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Computeralgebra |0 (DE-588)4010449-7 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Computeralgebra |0 (DE-588)4010449-7 |D s |
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| 700 | 1 | |a Sazdanović, Radmila |e Verfasser |4 aut | |
| 830 | 0 | |a K & E series on knots and everything |v 21 |w (DE-604)BV004608347 |9 21 | |
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Datensatz im Suchindex
| _version_ | 1804137939334070272 |
|---|---|
| adam_text | Titel: LinKnot
Autor: Jablan, Slavik Vlado
Jahr: 2007
Contents Preface v 1. Notation of Knots and Links 1 1.1 Basic graph theory...................... 1 1.2 Shadows of KLs ....................... 10 1.2.1 Gauss and Dowker code............... 16 1.3 KL diagrams......................... 25 1.4 Reidemeister moves...................... 40 1.5 Conway notation....................... 50 1.6 Classification of KLs ..................... 59 1.7 LinKnot functions and KL notation............ 66 1.8 Rational world and KL invariants............. 69 1.8.1 Chirality of rational KLs .............. 77 1.9 Unlinking number and unlinking gap............ 81 1.10 Prime and composite KLs .................. 119 1.11 Non-invertible KLs ...................... 125 1.11.1 Tangle types..................... 131 1.11.2 Non-invertible pretzel knots ............ 136 1.11.3 Non-invertible arborescent knots.......... 140 1.11.4 Non-invertible polyhedral knots.......... 142 1.12 Reduction of R-tangles.................... 145 1.12.1 KLs with unlinking number one.......... 148 1.13 Braids............................. 157 1.13.1 KLs and braids................... 161 1.14 Braid family representatives................. 165 1.14.1 Applications of minimum braids and braid family representatives.................... 179 vii
viii LinKnot 1.15 More KL invariants..................... 182 1.16 Borromean links....................... 187 2. Recognition and Generation of Knots and Links 195 2.1 Recognition of KLs ..................... 195 2.1.1 Group of KL ..................... 201 2.2 Polynomial invariants .................... 207 2.3 Vassiliev invariants...................... 219 2.4 Experimenting with KLs .................. 225 2.5 Derivation and classification of KLs ............ 227 2.6 Basic polyhedra and polyhedral KLs ............ 241 2.7 Basic polyhedra and non-algebraic tangles.........268 2.7.1 Generalized tangles................. 282 2.7.2 n-tangles and basic polyhedra........... 283 2.7.3 Non-algebraic tangle compositions and component algebra........................ 295 2.8 KL tables........................... 303 2.8.1 Non-alternating and almost alternating KLs . . . 307 2.9 Projections of KLs and chirality.............. 311 2.10 Families of undetectable KLs ................ 341 2.10.1 Detecting chirality of KLs by polynomial invariants 356 2.11 A dream— new KL tables.................. 363 3. History of Knot Theory and Applications of Knots and Links 375 3.1 History of knot theory.................... 375 3.2 Mirror curves......................... 383 3.2.1 Tamil treshold designs ............... 384 3.2.2 Tchokwe sand drawings............... 385 3.2.3 Construction of mirror curves ........... 388 3.2.4 Enumeration of mirror curves ........... 393 3.2.5 Lunda designs.................... 395 3.2.6 Polyominoes..................... 395 3.2.7 KLs and mirror curves............... 399 3.2.8 Mirror curves on different surfaces.........400 3.2.9 Mirror curves in art................. 401 3.2.10 KLs and self-avoiding curves............ 416 3.3 KLs and fullerenes...................... 426 3.3.1 General fullerenes, graphs, symmetry and isomers 427
Contents IX 3.3.2 5/6 fullerenes .................... 428 3.3.3 Knot theory and fullerenes...... 430 3.3.4 Nanotubes, conical and biconical fullerenes and their symmetry ................... 436 3.3.5 Fullerenes on other surfaces ............ 441 3.4 KLs and logic......................... 443 3.5 Waveforms .......................... 449 3.6 Knot automata........................ 453 Bibliography 459 Index 475
|
| adam_txt |
Titel: LinKnot
Autor: Jablan, Slavik Vlado
Jahr: 2007
Contents Preface v 1. Notation of Knots and Links 1 1.1 Basic graph theory. 1 1.2 Shadows of KLs . 10 1.2.1 Gauss and Dowker code. 16 1.3 KL diagrams. 25 1.4 Reidemeister moves. 40 1.5 Conway notation. 50 1.6 Classification of KLs . 59 1.7 LinKnot functions and KL notation. 66 1.8 Rational world and KL invariants. 69 1.8.1 Chirality of rational KLs . 77 1.9 Unlinking number and unlinking gap. 81 1.10 Prime and composite KLs . 119 1.11 Non-invertible KLs . 125 1.11.1 Tangle types. 131 1.11.2 Non-invertible pretzel knots . 136 1.11.3 Non-invertible arborescent knots. 140 1.11.4 Non-invertible polyhedral knots. 142 1.12 Reduction of R-tangles. 145 1.12.1 KLs with unlinking number one. 148 1.13 Braids. 157 1.13.1 KLs and braids. 161 1.14 Braid family representatives. 165 1.14.1 Applications of minimum braids and braid family representatives. 179 vii
viii LinKnot 1.15 More KL invariants. 182 1.16 Borromean links. 187 2. Recognition and Generation of Knots and Links 195 2.1 Recognition of KLs . 195 2.1.1 Group of KL . 201 2.2 Polynomial invariants . 207 2.3 Vassiliev invariants. 219 2.4 Experimenting with KLs . 225 2.5 Derivation and classification of KLs . 227 2.6 Basic polyhedra and polyhedral KLs . 241 2.7 Basic polyhedra and non-algebraic tangles.268 2.7.1 Generalized tangles. 282 2.7.2 n-tangles and basic polyhedra. 283 2.7.3 Non-algebraic tangle compositions and component algebra. 295 2.8 KL tables. 303 2.8.1 Non-alternating and almost alternating KLs . . . 307 2.9 Projections of KLs and chirality. 311 2.10 Families of undetectable KLs . 341 2.10.1 Detecting chirality of KLs by polynomial invariants 356 2.11 A dream— new KL tables. 363 3. History of Knot Theory and Applications of Knots and Links 375 3.1 History of knot theory. 375 3.2 Mirror curves. 383 3.2.1 Tamil treshold designs . 384 3.2.2 Tchokwe sand drawings. 385 3.2.3 Construction of mirror curves . 388 3.2.4 Enumeration of mirror curves . 393 3.2.5 Lunda designs. 395 3.2.6 Polyominoes. 395 3.2.7 KLs and mirror curves. 399 3.2.8 Mirror curves on different surfaces.400 3.2.9 Mirror curves in art. 401 3.2.10 KLs and self-avoiding curves. 416 3.3 KLs and fullerenes. 426 3.3.1 General fullerenes, graphs, symmetry and isomers 427
Contents IX 3.3.2 5/6 fullerenes . 428 3.3.3 Knot theory and fullerenes. 430 3.3.4 Nanotubes, conical and biconical fullerenes and their symmetry . 436 3.3.5 Fullerenes on other surfaces . 441 3.4 KLs and logic. 443 3.5 Waveforms . 449 3.6 Knot automata. 453 Bibliography 459 Index 475 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T21:45:26Z |
| indexdate | 2024-07-09T21:20:15Z |
| institution | BVB |
| isbn | 9789812772237 9812772235 |
| language | English |
| lccn | 2008295634 |
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| physical | ix, 485 p. ill. 24 cm |
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| series | K & E series on knots and everything |
| series2 | K & E series on knots and everything |
| spelling | Jablan, Slavik V. Verfasser aut LinKnot knot theory by computer Slavik Jablan, Radmila Sazdanović Hackensack, NJ [u.a.] World Scientific c2007 ix, 485 p. ill. 24 cm txt rdacontent n rdamedia nc rdacarrier K & E series on knots and everything 21 Includes bibliographical references (p. 459-474) and index Datenverarbeitung Knot theory Data processing Link theory Data processing Knotentheorie (DE-588)4164318-5 gnd rswk-swf Computeralgebra (DE-588)4010449-7 gnd rswk-swf Knotentheorie (DE-588)4164318-5 s Computeralgebra (DE-588)4010449-7 s DE-604 Sazdanović, Radmila Verfasser aut K & E series on knots and everything 21 (DE-604)BV004608347 21 http://www.loc.gov/catdir/toc/fy0803/2008295634.html Table of contents only HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016685299&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jablan, Slavik V. Sazdanović, Radmila LinKnot knot theory by computer K & E series on knots and everything Datenverarbeitung Knot theory Data processing Link theory Data processing Knotentheorie (DE-588)4164318-5 gnd Computeralgebra (DE-588)4010449-7 gnd |
| subject_GND | (DE-588)4164318-5 (DE-588)4010449-7 |
| title | LinKnot knot theory by computer |
| title_auth | LinKnot knot theory by computer |
| title_exact_search | LinKnot knot theory by computer |
| title_exact_search_txtP | LinKnot knot theory by computer |
| title_full | LinKnot knot theory by computer Slavik Jablan, Radmila Sazdanović |
| title_fullStr | LinKnot knot theory by computer Slavik Jablan, Radmila Sazdanović |
| title_full_unstemmed | LinKnot knot theory by computer Slavik Jablan, Radmila Sazdanović |
| title_short | LinKnot |
| title_sort | linknot knot theory by computer |
| title_sub | knot theory by computer |
| topic | Datenverarbeitung Knot theory Data processing Link theory Data processing Knotentheorie (DE-588)4164318-5 gnd Computeralgebra (DE-588)4010449-7 gnd |
| topic_facet | Datenverarbeitung Knot theory Data processing Link theory Data processing Knotentheorie Computeralgebra |
| url | http://www.loc.gov/catdir/toc/fy0803/2008295634.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016685299&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004608347 |
| work_keys_str_mv | AT jablanslavikv linknotknottheorybycomputer AT sazdanovicradmila linknotknottheorybycomputer |