Journal of Knot Theory and Its Ramifications最新文献

英文中文

Computation of the knot symmetric quandle and its application to the plat index of surface-links 绳结对称阶数的计算及其在表面链路 plat 指数中的应用

IF 0.5 4区数学 Q4 MATHEMATICS

Journal of Knot Theory and Its Ramifications

Pub Date : 2024-04-30 DOI: 10.1142/s0218216524500056

Jumpei Yasuda

A surface-link is a closed surface embedded in the 4-space, possibly disconnected or non-orientable. Every surface-link can be presented by the plat closure of a braided surface, which we call a plat form presentation. The knot symmetric quandle of a surface-link $F$ is a pair of a quandle and a good involution determined from $F$ . In this paper, we compute the knot symmetric quandle for surface-links using a plat form presentation. As an application, we show that for any integers $g \geq 0$ and $m \geq 2$ , there exist infinitely many distinct surface-knots of genus $g$ whose plat indices are $m$ .

曲面链接是嵌入 4 空间的封闭曲面，可能是断开的，也可能是不可定向的。每一个曲面链接都可以由一个编织曲面的plat closure呈现，我们称之为plat form 呈现。曲面链接 F 的结对称 quandle 是由 F 确定的一对 quandle 和一个好的反卷。作为应用，我们证明了对于任意整数 g≥0 和 m≥2，存在无穷多个不同的 g 属曲面结，其 plat 指数为 m。

{"title":"Computation of the knot symmetric quandle and its application to the plat index of surface-links","authors":"Jumpei Yasuda","doi":"10.1142/s0218216524500056","DOIUrl":"https://doi.org/10.1142/s0218216524500056","url":null,"abstract":"A surface-link is a closed surface embedded in the 4-space, possibly disconnected or non-orientable. Every surface-link can be presented by the plat closure of a braided surface, which we call a plat form presentation. The knot symmetric quandle of a surface-link <math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>F</mi></math> is a pair of a quandle and a good involution determined from <math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>F</mi></math>. In this paper, we compute the knot symmetric quandle for surface-links using a plat form presentation. As an application, we show that for any integers <math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>g</mi><mo>≥</mo><mn>0</mn></math> and <math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>m</mi><mo>≥</mo><mn>2</mn></math>, there exist infinitely many distinct surface-knots of genus <math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mi>g</mi></math> whose plat indices are <math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mi>m</mi></math>.","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":"9 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140828851","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

Coefficients of Catalan states of lattice crossing II: Applications of ΘA-state expansions 晶格交叉的加泰罗尼亚态系数 II： ΘA 态展开的应用

IF 0.5 4区数学 Q4 MATHEMATICS

Journal of Knot Theory and Its Ramifications

Pub Date : 2024-04-18 DOI: 10.1142/s0218216524500032

Mieczyslaw K. Dabkowski, Cheyu Wu

Plucking polynomial of a plane rooted tree with a delay function $α$ was introduced in 2014 by Przytycki. As shown in this paper, plucking polynomial factors when $α$ satisfies additional conditions. We use this result and $Θ_{A}$ -state expansion introduced in our previous work to derive new properties of coefficients $C (A)$ of Catalan states $C$ resulting from an $(m \times n)$ -lattice crossing $L (m, n)$ . In particular, we show that $C (A)$ factors when $C$ has arcs with some special properties. In many instances, this yields a more efficient way for computing $C (A)$ . As an application, we give closed-form formulas for coefficients of Catalan states of $L (m, 3)$ .

Przytycki 于 2014 年提出了具有延迟函数 α 的平面有根树的拔取多项式。正如本文所示，当 α 满足附加条件时，拔取多项式会产生因子。我们利用这一结果和之前工作中引入的 ΘA 态扩展，推导出 (m×n)- 格子交叉 L(m,n) 所产生的加泰罗尼亚态 C 的系数 C(A) 的新特性。特别是，我们证明了当 C 具有具有某些特殊性质的弧时，C(A) 的系数。在许多情况下，这将为计算 C(A) 提供更有效的方法。作为应用，我们给出了 L(m,3) 的加泰罗尼亚态系数的闭式公式。

{"title":"Coefficients of Catalan states of lattice crossing II: Applications of ΘA-state expansions","authors":"Mieczyslaw K. Dabkowski, Cheyu Wu","doi":"10.1142/s0218216524500032","DOIUrl":"https://doi.org/10.1142/s0218216524500032","url":null,"abstract":"Plucking polynomial of a plane rooted tree with a delay function <math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>α</mi></math> was introduced in 2014 by Przytycki. As shown in this paper, plucking polynomial factors when <math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>α</mi></math> satisfies additional conditions. We use this result and <math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi mathvariant=\"normal\">Θ</mi></mrow><mrow><mi>A</mi></mrow></msub></math>-state expansion introduced in our previous work to derive new properties of coefficients <math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mi>C</mi><mo stretchy=\"false\">(</mo><mi>A</mi><mo stretchy=\"false\">)</mo></math> of Catalan states <math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mi>C</mi></math> resulting from an <math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">(</mo><mi>m</mi><mo stretchy=\"false\">×</mo><mi>n</mi><mo stretchy=\"false\">)</mo></math>-lattice crossing <math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"><mi>L</mi><mo stretchy=\"false\">(</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo stretchy=\"false\">)</mo></math>. In particular, we show that <math altimg=\"eq-00009.gif\" display=\"inline\" overflow=\"scroll\"><mi>C</mi><mo stretchy=\"false\">(</mo><mi>A</mi><mo stretchy=\"false\">)</mo></math> factors when <math altimg=\"eq-00010.gif\" display=\"inline\" overflow=\"scroll\"><mi>C</mi></math> has arcs with some special properties. In many instances, this yields a more efficient way for computing <math altimg=\"eq-00011.gif\" display=\"inline\" overflow=\"scroll\"><mi>C</mi><mo stretchy=\"false\">(</mo><mi>A</mi><mo stretchy=\"false\">)</mo></math>. As an application, we give closed-form formulas for coefficients of Catalan states of <math altimg=\"eq-00012.gif\" display=\"inline\" overflow=\"scroll\"><mi>L</mi><mo stretchy=\"false\">(</mo><mi>m</mi><mo>,</mo><mn>3</mn><mo stretchy=\"false\">)</mo></math>.","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":"76 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140623948","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

Knot quandle decomposition along a torus 沿环状线的结quandle分解

IF 0.5 4区数学 Q4 MATHEMATICS

Journal of Knot Theory and Its Ramifications

Pub Date : 2024-03-22 DOI: 10.1142/s0218216523500980

Marco Bonatto, Alessia Cattabriga, Eva Horvat

We study the structure of the augmented fundamental quandle of a knot whose complement contains an incompressible torus. We obtain the relationship between the fundamental quandle of a satellite knot and the fundamental quandles/groups of its companion and pattern knots. General presentations of the fundamental quandles of a link in a solid torus, a link in a lens space and a satellite knot are described. In the last part of this paper, an algebraic approach to the study of affine quandles is presented and some known results about the Alexander module and quandle colorings are obtained.

我们研究了包含不可压缩环的补集的结的增强基序结构。我们得到了卫星结的基本群与它的伴结和模式结的基本群之间的关系。本文描述了实体环中的链接、透镜空间中的链接和卫星结的基本群的一般表述。在本文的最后一部分，介绍了研究仿射阶数的代数方法，并获得了关于亚历山大模数和阶数着色的一些已知结果。

引用次数: 0

Heegaard Floer invariants for cyclic 3-orbifolds 环状 3-orbifolds 的 Heegaard Floer 不变量

IF 0.5 4区数学 Q4 MATHEMATICS

Journal of Knot Theory and Its Ramifications

Pub Date : 2024-03-22 DOI: 10.1142/s0218216523501031

Saibal Ganguli, Mainak Poddar

We define a notion of Heegaard Floer homology for three-dimensional orbifolds with arbitrary cyclic singularities, generalizing the recent work of Biji Wong where the singular locus is assumed to be connected.

我们定义了具有任意循环奇点的三维轨道的 Heegaard Floer homology 概念，推广了 Biji Wong 的最新研究成果，其中假定奇点位置是连通的。

引用次数: 0

Presentations of diquandles and diquandle coloring invariants for solid torus knots and links 实心环结和链接的二阶和二阶着色不变式的呈现

IF 0.5 4区数学 Q4 MATHEMATICS

Journal of Knot Theory and Its Ramifications

Pub Date : 2024-03-15 DOI: 10.1142/s021821652350102x

Jieon Kim, Sang Youl Lee, Mohd Ibrahim Sheikh

A diquandle is a set equipped with two quandle operations interacting via a kind of distributive laws which come from Reidemeister moves on dichromatic links. This algebraic systems provide coloring invariants for dichromatic links. In this paper, we give explicit constructions of free diquandles and diquandle presentations, and then discuss Tietze transformations for the diquandle presentations. We also introduce the fundamental diquandles for dichromatic links. Particularly, we describe the fundamental diquandles and diquandle counting invariants for knots and links in the solid torus via annulus diagrams. We append the tables of diquandles and dikei’s of orders $\leq 5$ .

二阶梯（diquandle）是一个集合，其中有两个阶梯运算，这两个运算通过一种分配律相互作用，分配律来自二色链路上的雷德梅斯特移动。这种代数系统为二色环提供着色不变式。在本文中，我们给出了自由二叉和二叉呈现的明确构造，然后讨论了二叉呈现的 Tietze 变换。我们还介绍了二色链接的基本二叉。特别是，我们通过环形图描述了实心环中的结和链的基本二叉和二叉计数不变式。我们附录了阶数≤5 的二叉和二叉数表。

引用次数: 0

Bounds in simple hexagonal lattice and classification of 11-stick knots 简单六方格中的界限和 11 棍结的分类

IF 0.5 4区数学 Q4 MATHEMATICS

Journal of Knot Theory and Its Ramifications

Pub Date : 2024-02-27 DOI: 10.1142/s0218216523500979

Yueheng Bao, Ari Benveniste, Marion Campisi, Nicholas Cazet, Ansel Goh, Jiantong Liu, Ethan Sherman

The stick number and the edge length of a knot type in the simple hexagonal lattice (sh-lattice) are the minimal numbers of sticks and edges required, respectively, to construct a knot of the given type in sh-lattice. By introducing a linear transformation between lattices, we prove that for any given knot both values in the sh-lattice are strictly less than the values in the cubic lattice. Finally, we show that the only non-trivial $11$ -stick knots in the sh-lattice are the trefoil knot ( $3_{1}$ ) and the figure-eight knot ( $4_{1}$ ).

简单六方格（sh-lattice）中的绳结类型的棍数和边长分别是在 sh-lattice 中构建给定类型的绳结所需的最小棍数和边长。通过引入网格间的线性变换，我们证明了对于任何给定的结，sh-网格中的两个值都严格小于立方网格中的值。最后，我们证明了在 sh 格中唯一的非难 11 棍结是三叶草结 (31) 和八字结 (41)。

引用次数: 0

Representations of flat virtual braids which do not preserve the forbidden relations 不保留禁止关系的平面虚拟辫的表示

IF 0.5 4区数学 Q4 MATHEMATICS

Journal of Knot Theory and Its Ramifications

Pub Date : 2024-02-27 DOI: 10.1142/s0218216523500931

Valeriy Bardakov, Bogdan Chuzhinov, Ivan Emel’yanenkov, Maxim Ivanov, Elizaveta Markhinina, Timur Nasybullov, Sergey Panov, Nina Singh, Sergey Vasyutkin, Valeriy Yakhin, Andrei Vesnin

In the paper, we construct a representation <math altimg="eq-00001.gif" display="inline" overflow="scroll"><mi>𝜃</mi><mo>:</mo><msub><mrow><mstyle><mtext mathvariant="normal">FVB</mtext></mstyle></mrow><mrow><mi>n</mi></mrow></msub><mo>→</mo><mstyle><mtext mathvariant="normal">Aut</mtext></mstyle><mo stretchy="false">(</mo><msub><mrow><mi>F</mi></mrow><mrow><mn>2</mn><mi>n</mi></mrow></msub><mo stretchy="false">)</mo></math> of the flat virtual braid group <math altimg="eq-00002.gif" display="inline" overflow="scroll"><msub><mrow><mstyle><mtext mathvariant="normal">FVB</mtext></mstyle></mrow><mrow><mi>n</mi></mrow></msub></math> on <math altimg="eq-00003.gif" display="inline" overflow="scroll"><mi>n</mi></math> strands by automorphisms of the free group <math altimg="eq-00004.gif" display="inline" overflow="scroll"><msub><mrow><mi>F</mi></mrow><mrow><mn>2</mn><mi>n</mi></mrow></msub></math> with <math altimg="eq-00005.gif" display="inline" overflow="scroll"><mn>2</mn><mi>n</mi></math> generators which does not preserve the forbidden relations in the flat virtual braid group. This representation gives a positive answer to the problem formulated by Bardakov in the list of unsolved problems in virtual knot theory and combinatorial knot theory by Fenn et al.Also we find the set of normal generators of the groups <math altimg="eq-00006.gif" display="inline" overflow="scroll"><msub><mrow><mstyle><mtext mathvariant="normal">VP</mtext></mstyle></mrow><mrow><mi>n</mi></mrow></msub><mo stretchy="false">∩</mo><msub><mrow><mi>H</mi></mrow><mrow><mi>n</mi></mrow></msub></math> in <math altimg="eq-00007.gif" display="inline" overflow="scroll"><msub><mrow><mstyle><mtext mathvariant="normal">VB</mtext></mstyle></mrow><mrow><mi>n</mi></mrow></msub></math>, <math altimg="eq-00008.gif" display="inline" overflow="scroll"><msub><mrow><mstyle><mtext mathvariant="normal">FVP</mtext></mstyle></mrow><mrow><mi>n</mi></mrow></msub><mo stretchy="false">∩</mo><msub><mrow><mstyle><mtext mathvariant="normal">FH</mtext></mstyle></mrow><mrow><mi>n</mi></mrow></msub></math> in <math altimg="eq-00009.gif" display="inline" overflow="scroll"><msub><mrow><mstyle><mtext mathvariant="normal">FVB</mtext></mstyle></mrow><mrow><mi>n</mi></mrow></msub></math>, <math altimg="eq-00010.gif" display="inline" overflow="scroll"><msub><mrow><mstyle><mtext mathvariant="normal">GVP</mtext></mstyle></mrow><mrow><mi>n</mi></mrow></msub><mo stretchy="false">∩</mo><msub><mrow><mstyle><mtext mathvariant="normal">GH</mtext></mstyle></mrow><mrow><mi>n</mi></mrow></msub></math> in <math altimg="eq-00011.gif" display="inline" overflow="scroll"><msub><mrow><mstyle><mtext mathvariant="normal">GVB</mtext></mstyle></mrow><mrow><mi>n

在本文中，我们通过具有 2n 个生成子的自由群 F2n 的自动变形，构建了 n 股上平面虚辫群 FVBn 的表示𝜃:FVBn→Aut(F2n)，它不保留平面虚辫群中的禁止关系。同时，我们还发现了 VBn 中的 VPn∩Hn 群、FVBn 中的 FVPn∩FHn 群和 GVBn 中的 GVPn∩GHn 群的法向生成子集，它们在表示𝜃 的内核研究中起着重要作用。

引用次数: 0

An invariant of virtual trivalent spatial graphs 虚拟三价空间图的不变量

IF 0.5 4区数学 Q4 MATHEMATICS

Journal of Knot Theory and Its Ramifications

Pub Date : 2024-02-27 DOI: 10.1142/s0218216523500876

Evan Carr, Nancy Scherich, Sherilyn Tamagawa

We create an invariant of virtual $Y$ -oriented trivalent spatial graphs using colorings by virtual Niebrzydowski algebras. This paper generalizes the color invariants using virtual tribrackets and Niebrzydowski algebras by Nelson–Pico, and Graves-Nelson-T. We computed all tribrackets, Niebrzydowski algebras and virtual Niebrzydowski algebras of orders 3 and 4, and provide generative code for all data sets.

我们利用虚拟尼布日多夫斯基代数的着色创建了虚拟 Y 向三价空间图的不变式。本文推广了内尔松-皮科（Nelson-Pico）和格雷夫斯-内尔松-T（Graves-Nelson-T）使用虚拟三元组和尼布日多夫斯基（Niebrzydowski）代数的颜色不变式。我们计算了所有三元组、阶数为 3 和 4 的尼布日多夫斯基代数和虚拟尼布日多夫斯基代数，并提供了所有数据集的生成代码。

引用次数: 0

Modified symmetrized integral in G-coalgebras G 考量中的修正对称积分

IF 0.5 4区数学 Q4 MATHEMATICS

Journal of Knot Theory and Its Ramifications

Pub Date : 2024-01-24 DOI: 10.1142/s0218216523500827

Nathan Geer, Ngoc Phu Ha, Bertrand Patureau-Mirand

For $G$ a commutative group, we give a purely Hopf $G$ -coalgebra construction of $G$ -colored $3$ -manifolds invariants using the notion of modified integral.

对于交换群 G，我们利用修正积分的概念给出了一个纯霍普夫 G-代数构造的 G 色 3-manifolds不变式。

引用次数: 0

A new condition on the Jones polynomial of a fibered positive link 纤维正链琼斯多项式的新条件

IF 0.5 4区数学 Q4 MATHEMATICS

Journal of Knot Theory and Its Ramifications

Pub Date : 2024-01-06 DOI: 10.1142/s0218216523500797

Lizzie Buchanan

We give a new upper bound on the maximum degree of the Jones polynomial of a fibered positive link. In particular, we prove that the maximum degree of the Jones polynomial of a fibered positive knot is at most four times the minimum degree. Using this result, we can complete the classification of all knots of crossing number $\leq 12$ as positive or not positive, by showing that the seven remaining knots for which positivity was unknown are not positive. That classification was also done independently at around the same time by Stoimenow.

我们给出了纤维正链节的琼斯多项式最大度的新上限。特别是，我们证明了纤正结的琼斯多项式的最大度最多是最小度的四倍。利用这一结果，我们可以完成将交叉数≤12 的所有结划分为正结或非正结的工作，证明剩余的七个未知正结不是正结。大约在同一时间，斯托伊梅诺也独立完成了这一分类。

引用次数: 0

下一页尾页

类型

全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

数据库

全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

Journal of Knot Theory and Its Ramifications

全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.

﹀