Mathematical Modeling of the Weaving Structure Design

TL;DR

This paper introduces a mathematical framework for analyzing weaving structures using binary matrices, including an algorithm to identify key elements and describe their topological properties.

Contribution

It presents a new equivalence relation on binary matrices, an algorithm for identifying special elements, and applies these to understand weaving structure topology.

Findings

Defined an equivalence relation on binary matrices

Developed an algorithm to find special elements in the factor set

Applied results to describe weaving structure topology

Abstract

An equivalence relation in the set of all square binary matrices is described in this work. It is discussed a combinatoric problem about finding the cardinal number and the elements of the factor set according to this relation. We examine the possibility to get some special elements of this factor set. We propose an algorithm, which solves these problems. The results we have received are used to describe the topology of the different weaving structures.