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Journal of Knot Theory and Its Ramifications最新文献

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4-move distance of knots 4节移动距离
IF 0.5 4区 数学
Journal of Knot Theory and Its Ramifications Pub Date : 2022-06-24 DOI: 10.1142/s0218216522500493
T. Kanenobu, Hideo Takioka
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引用次数: 0
The Stick Number of Rail ARCS 钢轨电弧杆数
IF 0.5 4区 数学
Journal of Knot Theory and Its Ramifications Pub Date : 2022-06-22 DOI: 10.1142/S0218216523500311
Nicholas Cazet
{"title":"The Stick Number of Rail ARCS","authors":"Nicholas Cazet","doi":"10.1142/S0218216523500311","DOIUrl":"https://doi.org/10.1142/S0218216523500311","url":null,"abstract":"Consider two parallel lines $ell_1$ and $ell_2$ in $mathbb{R}^3$. A rail arc is an embedding of an arc in $mathbb{R}^3$ such that one endpoint is on $ell_1$, the other is on $ell_2$, and its interior is disjoint from $ell_1cupell_2$. Rail arcs are considered up to rail isotopies, ambient isotopies of $mathbb{R}^3$ with each self-homeomorphism mapping $ell_1$ and $ell_2$ onto themselves. When the manifolds and maps are taken in the piecewise linear category, these rail arcs are called stick rail arcs. The stick number of a rail arc class is the minimum number of sticks, line segments in a p.l. arc, needed to create a representative. This paper will calculate the stick numbers of rail arcs classes with a crossing number at most 2 and use a winding number invariant to calculate the stick numbers of infinitely many rail arc classes. Each rail arc class has two canonically associated knot classes, its under and over companions. This paper also introduces the rail stick number of knot classes, the minimum number of sticks needed to create a rail arcs whose under or over companion is the knot class. The rail stick number is calculated for all knot classes with crossing number at most 9. The stick number of multi-component rail arcs classes is considered as well as the lattice stick number of rail arcs.","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45030099","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Twist moves and the affine index polynomials of virtual knots 虚结的捻动与仿射指标多项式
IF 0.5 4区 数学
Journal of Knot Theory and Its Ramifications Pub Date : 2022-06-16 DOI: 10.1142/s0218216522500420
Younhee Choi, Dojin Kim, Myeong-Ju Jeong
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引用次数: 1
On Heegaard splittings of mapping torus and induced by open book decomposition 关于映射环面分裂和开卷分解的问题
IF 0.5 4区 数学
Journal of Knot Theory and Its Ramifications Pub Date : 2022-06-16 DOI: 10.1142/s0218216522500432
K. Du
{"title":"On Heegaard splittings of mapping torus and induced by open book decomposition","authors":"K. Du","doi":"10.1142/s0218216522500432","DOIUrl":"https://doi.org/10.1142/s0218216522500432","url":null,"abstract":"","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47532352","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
New Superbridge Index Calculations from Non-Minimal Realizations 基于非极小实现的新型超级桥梁指标计算
IF 0.5 4区 数学
Journal of Knot Theory and Its Ramifications Pub Date : 2022-06-14 DOI: 10.1142/S0218216522500638
C. Shonkwiler
{"title":"New Superbridge Index Calculations from Non-Minimal Realizations","authors":"C. Shonkwiler","doi":"10.1142/S0218216522500638","DOIUrl":"https://doi.org/10.1142/S0218216522500638","url":null,"abstract":"Previous work [21] used polygonal realizations of knots to reduce the problem of computing the superbridge number of a realization to a linear programming problem, leading to new sharp upper bounds on the superbridge index of a number of knots. The present work extends this technique to polygonal realizations with an odd number of edges and determines the exact superbridge index of many new knots, including the majority of the 9-crossing knots for which it was previously unknown and, for the first time, several 12-crossing knots. Interestingly, at least half of these superbridge-minimizing polygonal realizations do not minimize the stick number of the knot; these seem to be the first such examples. Appendix A gives a complete summary of what is currently known about superbridge indices of prime knots through 10 crossings and Appendix B gives all knots through 16 crossings for which the superbridge index is known.","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45425683","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Embedding tangles and the Kauffman bracket polynomials 嵌入缠结和考夫曼括号多项式
IF 0.5 4区 数学
Journal of Knot Theory and Its Ramifications Pub Date : 2022-06-05 DOI: 10.1142/s0218216522500389
Myeong-Ju Jeong, Y. Kim
{"title":"Embedding tangles and the Kauffman bracket polynomials","authors":"Myeong-Ju Jeong, Y. Kim","doi":"10.1142/s0218216522500389","DOIUrl":"https://doi.org/10.1142/s0218216522500389","url":null,"abstract":"","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48288202","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Triple Point Number of Surface-Links in Yoshikawa's Table 吉川表中面链的三点数
IF 0.5 4区 数学
Journal of Knot Theory and Its Ramifications Pub Date : 2022-05-23 DOI: 10.1142/s0218216523500372
Nicholas Cazet
{"title":"On the Triple Point Number of Surface-Links in Yoshikawa's Table","authors":"Nicholas Cazet","doi":"10.1142/s0218216523500372","DOIUrl":"https://doi.org/10.1142/s0218216523500372","url":null,"abstract":"Yoshikawa made a table of knotted surfaces in R^4 with ch-index 10 or less. This remarkable table is the first to enumerate knotted surfaces analogous to the classical prime knot table. A broken sheet diagram of a surface-link is a generic projection of the surface in R^3 with crossing information along its singular set. The minimal number of triple points among all broken sheet diagrams representing a given surface-knot is its triple point number. This paper compiles the known triple point numbers of the surface-links represented in Yoshikawa's table and calculates or provides bounds on the triple point number of the remaining surface-links.","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47059099","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Behind Maths: federating research(ers) 数学背后：联合研究
IF 0.5 4区 数学
Journal of Knot Theory and Its Ramifications Pub Date : 2022-05-20 DOI: 10.1142/s0218216522400077
P. Bellingeri
{"title":"Behind Maths: federating research(ers)","authors":"P. Bellingeri","doi":"10.1142/s0218216522400077","DOIUrl":"https://doi.org/10.1142/s0218216522400077","url":null,"abstract":"","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41515221","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Some computational aspects in the work of Patrick Dehornoy Patrick Dehornoy工作中的一些计算方面
IF 0.5 4区 数学
Journal of Knot Theory and Its Ramifications Pub Date : 2022-05-20 DOI: 10.1142/s0218216522400053
J. González-Meneses
{"title":"Some computational aspects in the work of Patrick Dehornoy","authors":"J. González-Meneses","doi":"10.1142/s0218216522400053","DOIUrl":"https://doi.org/10.1142/s0218216522400053","url":null,"abstract":"","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44405446","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Birth of Garside groups in memory of Patrick Dehornoy 纪念Patrick Dehornoy的Garside团体的诞生
IF 0.5 4区 数学
Journal of Knot Theory and Its Ramifications Pub Date : 2022-05-20 DOI: 10.1142/s0218216522400041
L. Paris
{"title":"Birth of Garside groups in memory of Patrick Dehornoy","authors":"L. Paris","doi":"10.1142/s0218216522400041","DOIUrl":"https://doi.org/10.1142/s0218216522400041","url":null,"abstract":"","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":"17 3","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41302468","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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