虚拟三价空间图的不变量

IF 0.3 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

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引用次数: 0

摘要

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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An invariant of virtual trivalent spatial graphs

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.

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来源期刊

Journal of Knot Theory and Its Ramifications 数学-数学

CiteScore

0.80

自引率

40.00%

发文量

127

审稿时长

4-8 weeks

期刊介绍： This Journal is intended as a forum for new developments in knot theory, particularly developments that create connections between knot theory and other aspects of mathematics and natural science. Our stance is interdisciplinary due to the nature of the subject. Knot theory as a core mathematical discipline is subject to many forms of generalization (virtual knots and links, higher-dimensional knots, knots and links in other manifolds, non-spherical knots, recursive systems analogous to knotting). Knots live in a wider mathematical framework (classification of three and higher dimensional manifolds, statistical mechanics and quantum theory, quantum groups, combinatorics of Gauss codes, combinatorics, algorithms and computational complexity, category theory and categorification of topological and algebraic structures, algebraic topology, topological quantum field theories). Papers that will be published include: -new research in the theory of knots and links, and their applications; -new research in related fields; -tutorial and review papers. With this Journal, we hope to serve well researchers in knot theory and related areas of topology, researchers using knot theory in their work, and scientists interested in becoming informed about current work in the theory of knots and its ramifications.