Random knots using Chebyshev billiard table diagrams
Topology and its Applications 194 (2015) 4-21 We use the Chebyshev knot diagram model of Koseleff and Pecker in order to introduce a random knot diagram model by assigning the crossings to be positive or negative uniformly at random. We give a formula for the probability of choosing a knot at random...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext bestellen |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | |
| container_start_page | |
| container_title | |
| container_volume | |
| creator | Cohen, Moshe Krishnan, Sunder Ram |
| description | Topology and its Applications 194 (2015) 4-21 We use the Chebyshev knot diagram model of Koseleff and Pecker in order to
introduce a random knot diagram model by assigning the crossings to be positive
or negative uniformly at random. We give a formula for the probability of
choosing a knot at random among all knots with bridge index at most 2.
Restricted to this class, we define internal and external reduction moves that
decrease the number of crossings of the diagram. We make calculations based on
our formula, showing the numerics in graphs and providing evidence for our
conjecture that the probability of any knot appearing in this model decays to
zero as the number of crossings goes to infinity. |
| doi_str_mv | 10.48550/arxiv.1505.07681 |
| format | Article |
| fullrecord | <record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_1505_07681</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1505_07681</sourcerecordid><originalsourceid>FETCH-LOGICAL-a671-ee76ed225c3ed1fbd8af390b86812b04b2f666f3f66c21edf9552e39603b6fd3</originalsourceid><addsrcrecordid>eNotzk1uwjAUBGBvWFSUA3SFL5Dgn9hJllUEFAkJCdhHz_g5sUgCsgGV20Mpm5ndzEfIF2dpVijFZhB-_S3liqmU5brgHyTbwmBPPT0Op0uk1-iHhlYtmnts8UaN7zoPwdILmA6p9dAE6OMnGTnoIk7ePSa7xXxf_STrzXJVfa8T0DlPEHONVgh1kGi5M7YAJ0tmiuexMCwzwmmtnXzmQXC0rlRKoCw1k0Y7K8dk-r_6Utfn4HsI9_pPX7_08gFcYD-f</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Random knots using Chebyshev billiard table diagrams</title><source>arXiv.org</source><creator>Cohen, Moshe ; Krishnan, Sunder Ram</creator><creatorcontrib>Cohen, Moshe ; Krishnan, Sunder Ram</creatorcontrib><description>Topology and its Applications 194 (2015) 4-21 We use the Chebyshev knot diagram model of Koseleff and Pecker in order to
introduce a random knot diagram model by assigning the crossings to be positive
or negative uniformly at random. We give a formula for the probability of
choosing a knot at random among all knots with bridge index at most 2.
Restricted to this class, we define internal and external reduction moves that
decrease the number of crossings of the diagram. We make calculations based on
our formula, showing the numerics in graphs and providing evidence for our
conjecture that the probability of any knot appearing in this model decays to
zero as the number of crossings goes to infinity.</description><identifier>DOI: 10.48550/arxiv.1505.07681</identifier><language>eng</language><subject>Mathematics - Combinatorics ; Mathematics - Geometric Topology ; Mathematics - Probability</subject><creationdate>2015-05</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1505.07681$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1505.07681$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Cohen, Moshe</creatorcontrib><creatorcontrib>Krishnan, Sunder Ram</creatorcontrib><title>Random knots using Chebyshev billiard table diagrams</title><description>Topology and its Applications 194 (2015) 4-21 We use the Chebyshev knot diagram model of Koseleff and Pecker in order to
introduce a random knot diagram model by assigning the crossings to be positive
or negative uniformly at random. We give a formula for the probability of
choosing a knot at random among all knots with bridge index at most 2.
Restricted to this class, we define internal and external reduction moves that
decrease the number of crossings of the diagram. We make calculations based on
our formula, showing the numerics in graphs and providing evidence for our
conjecture that the probability of any knot appearing in this model decays to
zero as the number of crossings goes to infinity.</description><subject>Mathematics - Combinatorics</subject><subject>Mathematics - Geometric Topology</subject><subject>Mathematics - Probability</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzk1uwjAUBGBvWFSUA3SFL5Dgn9hJllUEFAkJCdhHz_g5sUgCsgGV20Mpm5ndzEfIF2dpVijFZhB-_S3liqmU5brgHyTbwmBPPT0Op0uk1-iHhlYtmnts8UaN7zoPwdILmA6p9dAE6OMnGTnoIk7ePSa7xXxf_STrzXJVfa8T0DlPEHONVgh1kGi5M7YAJ0tmiuexMCwzwmmtnXzmQXC0rlRKoCw1k0Y7K8dk-r_6Utfn4HsI9_pPX7_08gFcYD-f</recordid><startdate>20150528</startdate><enddate>20150528</enddate><creator>Cohen, Moshe</creator><creator>Krishnan, Sunder Ram</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20150528</creationdate><title>Random knots using Chebyshev billiard table diagrams</title><author>Cohen, Moshe ; Krishnan, Sunder Ram</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a671-ee76ed225c3ed1fbd8af390b86812b04b2f666f3f66c21edf9552e39603b6fd3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Mathematics - Combinatorics</topic><topic>Mathematics - Geometric Topology</topic><topic>Mathematics - Probability</topic><toplevel>online_resources</toplevel><creatorcontrib>Cohen, Moshe</creatorcontrib><creatorcontrib>Krishnan, Sunder Ram</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Cohen, Moshe</au><au>Krishnan, Sunder Ram</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Random knots using Chebyshev billiard table diagrams</atitle><date>2015-05-28</date><risdate>2015</risdate><abstract>Topology and its Applications 194 (2015) 4-21 We use the Chebyshev knot diagram model of Koseleff and Pecker in order to
introduce a random knot diagram model by assigning the crossings to be positive
or negative uniformly at random. We give a formula for the probability of
choosing a knot at random among all knots with bridge index at most 2.
Restricted to this class, we define internal and external reduction moves that
decrease the number of crossings of the diagram. We make calculations based on
our formula, showing the numerics in graphs and providing evidence for our
conjecture that the probability of any knot appearing in this model decays to
zero as the number of crossings goes to infinity.</abstract><doi>10.48550/arxiv.1505.07681</doi><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext_linktorsrc |
| identifier | DOI: 10.48550/arxiv.1505.07681 |
| ispartof | |
| issn | |
| language | eng |
| recordid | cdi_arxiv_primary_1505_07681 |
| source | arXiv.org |
| subjects | Mathematics - Combinatorics Mathematics - Geometric Topology Mathematics - Probability |
| title | Random knots using Chebyshev billiard table diagrams |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-20T14%3A51%3A53IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-arxiv_GOX&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Random%20knots%20using%20Chebyshev%20billiard%20table%20diagrams&rft.au=Cohen,%20Moshe&rft.date=2015-05-28&rft_id=info:doi/10.48550/arxiv.1505.07681&rft_dat=%3Carxiv_GOX%3E1505_07681%3C/arxiv_GOX%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true |