{"?xml":{"@version":"1.0"},"edm:RDF":{"@xmlns:dc":"http://purl.org/dc/elements/1.1/","@xmlns:edm":"http://www.europeana.eu/schemas/edm/","@xmlns:wgs84_pos":"http://www.w3.org/2003/01/geo/wgs84_pos","@xmlns:foaf":"http://xmlns.com/foaf/0.1/","@xmlns:rdaGr2":"http://rdvocab.info/ElementsGr2","@xmlns:oai":"http://www.openarchives.org/OAI/2.0/","@xmlns:owl":"http://www.w3.org/2002/07/owl#","@xmlns:rdf":"http://www.w3.org/1999/02/22-rdf-syntax-ns#","@xmlns:ore":"http://www.openarchives.org/ore/terms/","@xmlns:skos":"http://www.w3.org/2004/02/skos/core#","@xmlns:dcterms":"http://purl.org/dc/terms/","edm:WebResource":[{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-1EWDSOSO/49a20154-8f2e-497d-a5ad-51407dc80a92/PDF","dcterms:extent":"919 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-1EWDSOSO/3571a5d6-5d86-4ec2-b34f-7dcc7049d08b/TEXT","dcterms:extent":"75 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-1EWDSOSO/7c4e3ea0-8547-4b55-a8e3-554a9e151a91/PDF","dcterms:extent":"122 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-1EWDSOSO/3299953b-7215-4fd1-8ba6-3228a9bf3b68/TEXT","dcterms:extent":"4 KB"}],"edm:TimeSpan":{"@rdf:about":"2008-2025","edm:begin":{"@xml:lang":"en","#text":"2008"},"edm:end":{"@xml:lang":"en","#text":"2025"}},"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:doc-1EWDSOSO","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2023","dc:creator":["Boden, Hans U.","Shimoda, Matthew"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:23"},{"@xml:lang":"sl","#text":"P1.10 (27 str.)"}],"dc:identifier":["DOI:10.26493/1855-3974.2730.6ac","COBISSID_HOST:149286659","ISSN:1855-3966","URN:URN:NBN:SI:doc-1EWDSOSO"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije"},"dc:subject":[{"@xml:lang":"sl","#text":"barvni Jonesov polinom"},{"@xml:lang":"en","#text":"braids"},{"@xml:lang":"en","#text":"colored Jones polynomial"},{"@xml:lang":"sl","#text":"enostaven sprehod"},{"@xml:lang":"en","#text":"knots"},{"@xml:lang":"sl","#text":"pletenice"},{"@xml:lang":"en","#text":"simple walk"},{"@xml:lang":"sl","#text":"vozli"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Braid representatives minimizing the number of simple walks|"},"dc:description":[{"@xml:lang":"sl","#text":"Given a knot, we find the braid representative that minimizes the number of simple walks. Such braids lead to an efficient method for computing the colored Jones polynomial of the knot, following an approach developed by Armond and implemented by Hajij and Levitt. We use this method to compute the colored Jones polynomial in closed form for the knots ?$5_2$?, ?$6_1$?, and ?$7_2$?. The set of simple walks can change under reflection, rotation, and cyclic permutation of the braid, and we prove an invariance property which relates the simple walks of a braid to those of its reflection under cyclic permutation. We study the growth rate of the number of simple walks for families of torus knots. Finally, we present a table of braid words that minimize the number of simple walks for knots up to 13 crossings"},{"@xml:lang":"sl","#text":"V članku razvijemo metode za določitev predstavnika pletenic, ki minimizira število enostavnih sprehodov v danem vozlu. Takšne pletenice vodijo k učinkoviti metodi za izračun barvnega Jonesovega polinoma vozla, s čimer sledimo pristopu, ki ga je razvil Armond, implementirala pa sta ga Hajij in Levitt. To metodo uporabimo za izračun barvnega Jonesovega polinoma v sklenjeni obliki za vozle ?$5_2$?, ?$6_1$?, in ?$7_2$?. Množica enostavnih vozlov enostavnih sprehodov se lahko spremeni z zrcaljenjem, rotacijo in ciklično permutacijo pletenic; dokažemo invariantno lastnost, ki povezuje enostavne sprehode pletenice s tistimi, ki pripadajo njeni zrcalni obliki pri ciklični permutaciji. Preučujemo stopnjo rasti števila enostavnih sprehodov za družine torusnih vozlov. Nazadnje predstavimo tabelo pleteničnih besed, ki minimizirajo število enostavnih sprehodov za vozle z do 13 križišči"}],"edm:type":"TEXT","dc:type":[{"@xml:lang":"sl","#text":"znanstveno časopisje"},{"@xml:lang":"en","#text":"journals"},{"@rdf:resource":"http://www.wikidata.org/entity/Q361785"}]},"ore:Aggregation":{"@rdf:about":"http://www.dlib.si/?URN=URN:NBN:SI:doc-1EWDSOSO","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-1EWDSOSO"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-1EWDSOSO/49a20154-8f2e-497d-a5ad-51407dc80a92/PDF"},"edm:rights":{"@rdf:resource":"http://creativecommons.org/licenses/by/4.0/"},"edm:provider":"Slovenian National E-content Aggregator","edm:intermediateProvider":{"@xml:lang":"en","#text":"National and University Library of Slovenia"},"edm:dataProvider":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije"},"edm:object":{"@rdf:resource":"http://www.dlib.si/streamdb/URN:NBN:SI:doc-1EWDSOSO/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-1EWDSOSO"}}}}