%0 Journal Article
%T 一类特殊链环的Kauffman多项式<br>The Kauffman Polynomials of a Special Class of Links
%A 徐芷微
%J Advances in Applied Mathematics
%P 4153-4165
%@ 2324-8009
%D 2023
%I Hans Publishing
%R 10.12677/AAM.2023.12100407
%X Kauffman多项式在纽结理论中占据一定地位，是纽结和链环中最有用的双变量Laurent多项式不变量之一，其已经成为量子拓扑的基本构建块。本文主要研究一类特殊不定向链环——复叠链环，研究了这类链环的Kauffman多项式以及Kauffman多项式对应的生成函数。借助直线型链环的Kauffman多项式对复叠链环的Kauffman多项式进行计算，这为研究定向复叠链环的Kauffman多项式以及BLM/Ho多项式奠定基础。<br />
The Kauffman polynomial is probably the most useful two-variable polynomial invariants of knots and links. It generalizes the Jones polynomial, and it has become basic building blocks of quantum topology. In this paper, we mainly study a special type of links—the covering links, and we study the Kauffman polynomials of the link and the corresponding generating functions. The Kauffman poly-nomials of the covering links is calculated by using the Kauffman polynomials of linear links, which lays a foundation for the study of Kauffman polynomials and BLM/Ho polynomials of the oriented covering links.
%K Kauffman多项式，递归关系式，生成函数<br>Kauffman Polynomial
%K Recurrence Relation
%K Generating Function
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=73483