Characterization of the OU matrix of a braid diagram

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-05-27 DOI:10.1016/j.topol.2025.109440

Ayaka Shimizu , Yoshiro Yaguchi

引用次数: 0

Abstract

The OU matrix of a braid diagram is a square matrix that represents the number of over/under crossings of each pair of strands. In this paper, the OU matrix of a pure braid diagram is characterized for up to 5 strands. As an application, the crossing matrix of a positive pure braid is also characterized for up to 5 strands. Moreover, a standard form of the OU matrix is given and characterized for general braids of up to 5 strands.

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编织图的OU矩阵的表征

编织图的OU矩阵是一个方阵，表示每对线交叉的次数。本文对纯编织图的OU矩阵进行了多达5股的刻画。作为一种应用，正纯编织的交叉矩阵也具有多达5股的特征。此外，给出了一种标准形式的OU矩阵，并对其进行了表征。

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

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.