A bracket polynomial for 2-tangle shadows

关于闭4-缠结括号多项式递归计算的注记

A note on the recursive computation of the bracket polynomial for closed 4-tangles

该研究针对4-缠结阴影，通过自身n次连接与特定闭合操作形成纽结，利用考夫曼4-股图幺半群基的状态矩阵递归计算所得纽结的考夫曼括号多项式。

A one-variable bracket polynomial for some Turk's head knots

We compute the Kauffman bracket polynomial of the three-lead Turk's head, the chain sinnet and the figure-eight chain shadow diagrams. Each of these knots can in fact be constructed by repeatedly concatenating the same 3-tangle, respectively, then taking the closure. The bracket is then evaluated by expressing the state diagrams of the concerned 3-tangle by means of the Kauffman monoid diagram's elements.

Celtic 链环阴影 $CK_4^{2n}$ 的括号多项式

The bracket polynomial of the Celtic link shadow $CK_4^{2n}$

本文利用基于图形恒等式的递推关系和 4-tangle 代数框架两种互补方法，推导了 Celtic 链环 $CK_4^{2n}$ 阴影的 Kauffman 括号多项式。

A bracket polynomial for graphs. III. Vertex weights

In earlier work the Kauffman bracket polynomial was extended to an invariant of marked graphs, i.e., looped graphs whose vertices have been partitioned into two classes (marked and not marked). The marked-graph bracket polynomial is readily modified to handle graphs with weighted vertices. We present formulas that simplify the computation of this weighted bracket for graphs that contain twin vertices or are constructed using graph composition, and we show that graph composition corresponds to the construction of a link diagram from tangles.