{"title":"虚拟三价空间图的不变量","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":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-02-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/s0218216523500876\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s0218216523500876","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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。
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.
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