{"title":"关于织结的解结数和区域解结数的说明","authors":"Ayaka Shimizu, Amrendra Gill, Sahil Joshi","doi":"arxiv-2408.14938","DOIUrl":null,"url":null,"abstract":"A weaving knot is an alternating knot whose minimal diagram is a closed braid\nof a lattice-like pattern. In this paper, upper bounds of the unknotting number\nand the region unknotting number for some families of weaving knots are given\nby diagrammatical and combinatorial examination of the warping degree of\nweaving knot diagrams.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"132 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A note on the unknotting number and the region unknotting number of weaving knots\",\"authors\":\"Ayaka Shimizu, Amrendra Gill, Sahil Joshi\",\"doi\":\"arxiv-2408.14938\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A weaving knot is an alternating knot whose minimal diagram is a closed braid\\nof a lattice-like pattern. In this paper, upper bounds of the unknotting number\\nand the region unknotting number for some families of weaving knots are given\\nby diagrammatical and combinatorial examination of the warping degree of\\nweaving knot diagrams.\",\"PeriodicalId\":501271,\"journal\":{\"name\":\"arXiv - MATH - Geometric Topology\",\"volume\":\"132 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Geometric Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2408.14938\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Geometric Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.14938","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A note on the unknotting number and the region unknotting number of weaving knots
A weaving knot is an alternating knot whose minimal diagram is a closed braid
of a lattice-like pattern. In this paper, upper bounds of the unknotting number
and the region unknotting number for some families of weaving knots are given
by diagrammatical and combinatorial examination of the warping degree of
weaving knot diagrams.
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