形式语言和形式文法作为语言学，逻辑学，计算机科学等学科的基础理论，由于其高度离散性的特质，得到了数学家，包括组合学家的广泛关注。适用于组合结构的上下文无关文法和形式导数理论的建立，以及相应的文法标号方法的发展作为形式文法在组合数学中的应用，为诸多学者在解决排列，树，对称函数及组合多项式等问题时提供了便捷的途径。结合申请人的研究基础，本项目内容主要涉及上下文无关文法及文法标号在排列统计量研究中的应用，具体包括：发展非下降位型统计量的文法方法；利用文法工具确定非下降位型统计量与下降位型统计量的联合分布生成函数；完善排列多项式γ-正性的文法方法及建立γ-正性展开式上的文法标号。本项目的成功开展有助于扩大文法理论在排列统计量研究中的应用范围，为相关问题的解决提供新角度，新思路和新工具，进而使文法理论适用于更多的组合结构，促进语言学，计算机科学等学科与组合数学的交叉融合。

As the basic concepts in linguistics, logic and computer science, the formal languages and the formal grammars have been also widely concerned by mathematicians, including combinatorialists, because of their highly discrete characteristics. The establishment of the theory of context-free grammars and formal derivatives on combinatorial structures and the development of the corresponding grammatical labelings are regarded as the profound applications of formal grammars in combinatorics, which provides direct and convenient approaches for many researchers to solve the problems related to permutations, trees, symmetric functions and combinatorial polynomials. Based on the research experience of the applicant, this project mainly involves the applications of context-free grammars and grammar labelings in the study of permutation statistics, including developing the grammatical methods on non-descent-type statistics, determining the generating functions of joint distributions of non-descent-type and descent-type statistics with grammatical tools, and improving the grammatical methods on γ-positivity of permutation polynomials and establishing grammatical labelings on γ-positivity expansions. The successful execution of this project will help to expand the applications of grammatical theory in the research of permutation statistics, provide new perspectives, ideas and tools for solving related problems, and make grammatical theory adaptive for more combinatorial structures, which can promote the cross amalgamation of linguistics, computer science and other disciplines with combinatorics.