Words and noncommutative algebraic combinatorics

单词和非对易代数组合学：*单词出现在语言学、计算机科学和通信中。它们本身也是一个数学概念。它们对非对易概念至关重要，非对易在当代*数学科学中扮演着重要角色。事实上，非对易性是这样一种性质，即两个运算的效果取决于完成这些运算的顺序。这是单词字母的典型特征：字母的顺序很重要。因此，非对易代数结构中的计算依赖于词的组合性质。它们还被用来对平面中的图像进行编码。他们的数学研究是这个项目的中心，该项目是在纯数学和应用数学领域。

Words and noncommutative algebraic combinatorics:***Words appear in linguistics, in computer science and in communications. They are also a mathematical concept***for itself. They are crucial for the notion of noncommutativity, which plays an important role in the contemporary***mathematical sciences. Indeed, noncommutativity is the property that the effect of two operations depends on the order where these operations are done. This is a typical property of the letters of a word: the order of letter matters. Thus, computations in noncommutative algebraic structures rest on combinatorial properties of words. They are also used to encode images in the plane. Their mathematical study is at the center of the present program, which is in the area of pure and applied mathematics.*****