Studies on fabric weave representation by group theory

This paper introduces group into fabric weave and proposes a new fabric weave representation method by group theory.Firstly,on the basis of set theory and mapping relationship between the set of weft serial orders and the set of warp float serial orders,it utilizes permutation to define fabric weave,and builds its mathematical model.Secondly,it takes weaves with the same weft repeat as the main object investigated,classifies them into weave Ⅰ and weave Ⅱ,and defines composite operator between these two types of weaves.Then it investigates the group structure and relative operations of the corresponding type of weaves under the operator defined.Finally,it discusses the method of fabric weave representation with some examples.The method explores a new digital way to represent fabric weave consequently.