The coefficients of the Jones polynomial

IF 0.3 4区数学 Q4 MATHEMATICS

Journal of Knot Theory and Its Ramifications Pub Date : 2023-08-01 DOI:10.1142/s0218216523500530

V. Manathunga

引用次数: 0

Abstract

It has been known that the coefficients of the series expansion of the Jones polynomial evaluated at [Formula: see text] are rational-valued Vassiliev invariants. In this paper, we calculate minimal multiplying factor, [Formula: see text], needed for these rational-valued invariants to become integer-valued Vassiliev invariants. By doing that, we obtain a set of integer-valued Vassiliev invariants.

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琼斯多项式的系数

众所周知，琼斯多项式级数展开式的系数在[公式:见文本]处是有理值Vassiliev不变量。在本文中，我们计算了这些有理值不变量变为整数值Vassiliev不变量所需的最小乘因子[公式:见文]。通过这样做，我们得到了一组整数值瓦西里耶夫不变量。

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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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.