Words and noncommutative algebraic combinatorics

单词和非交换代数组合： 单词出现在语言学、计算机科学和通信中。它们也是一个数学概念 为自己。它们对于非对易性的概念至关重要，而非对易性在当代数学中起着重要作用。 数学科学事实上，非交换性是两个操作的效果取决于这些操作完成的顺序的性质。这是单词字母的一个典型属性：字母的顺序很重要。因此，非交换代数结构中的计算依赖于词的组合性质。它们也被用于在平面中编码图像。他们的数学研究是本计划的中心，这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.