{"title":"An invariant of virtual trivalent spatial graphs","authors":"Evan Carr, Nancy Scherich, Sherilyn Tamagawa","doi":"10.1142/s0218216523500876","DOIUrl":null,"url":null,"abstract":"<p>We create an invariant of virtual <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>Y</mi></math></span><span></span>-oriented trivalent spatial graphs using colorings by <i>virtual Niebrzydowski algebras</i>. This paper generalizes the color invariants using <i>virtual tribrackets</i> and <i>Niebrzydowski algebras</i> 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.</p>","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":"81 1","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Knot Theory and Its Ramifications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s0218216523500876","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We create an invariant of virtual -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.
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.
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