| 词条 | Knot tabulation |
| 释义 |
Ever since Sir William Thomson's vortex theory, mathematicians have tried to classify and tabulate all possible knots. As of May 2008, all prime knots up to 16 crossings have been tabulated.[1] Beginnings{{main|History of knot theory}}In an attempt to make a periodic table of the elements, P. G. Tait, C. N. Little and others started counting all possible knots.[1] Perko pair{{main|Perko pair}}In 1974 Perko discovered a duplication in the Tait-Little tables, called the Perko pair. New methodsJim Hoste, Jeff Weeks, and Morwen Thistlethwaite used computer searches to count all knots with 16 or fewer crossings. This research was performed separately using two different algorithms on different computers, lending support to the correctness of its results. Both counts found 1701936 prime knots (including the unknot) with up to 16 crossings.[2] Starting with three crossings (the minimum for any nontrivial knot), the number of prime knots for each number of crossings is 1, 1, 2, 3, 7, 21, 49, 165, 552, 2176, 9988, 46972, 253293, 1388705, ... {{OEIS|A002863}} See also
References1. ^http://pzacad.pitzer.edu/~jhoste/HosteWebPages/downloads/Enumeration.pdf {{Knot theory}}{{DEFAULTSORT:Knot Tabulation}}2. ^1 {{citation |last1 = Hoste |first1 = Jim |last2 = Thistlethwaite |first2 = Morwen |last3 = Weeks |first3 = Jeff |doi = 10.1007/BF03025227 |issue = 4 |journal = The Mathematical Intelligencer |mr = 1646740 |pages = 33–48 |title = The first 1,701,936 knots |url = http://www.math.harvard.edu/~ctm/home/text/class/harvard/101/05/html/home/pdf/first.pdf |volume = 20 |year = 1998 |deadurl = yes |archiveurl = https://web.archive.org/web/20131215102511/http://www.math.harvard.edu/~ctm/home/text/class/harvard/101/05/html/home/pdf/first.pdf |archivedate = 2013-12-15 |df = }}. 1 : Knot theory |
| 随便看 |
|
开放百科全书收录14589846条英语、德语、日语等多语种百科知识，基本涵盖了大多数领域的百科知识，是一部内容自由、开放的电子版国际百科全书。