关于排列、杨表、格路与树等组合结构及相关统计量的研究是当前国际上计数组合学研究的热点问题。这些问题不仅与代数、几何等其它数学分支联系紧密，并且在计算机科学和分子生物学等领域有广泛的应用背景。本项目中我们将致力于用构造性方法研究这些结构及其上统计量的计数。具体内容包括给定形状的杨表的上的major和amajor指标的计数，major多项式与amajor多项式的对称性与单峰性，格路中的统计量与限制钩长形状的杨表的计数，给定限制条件的格路的均匀分布，以及树的计数等问题。

Enumerations on structures such as tableaux, trees, lattice paths and permutations, and their related statistics are very popular topics in combinatorics during the recent decades. There are application backgrounds of these problems in computer science and bioinformatics. In this project we will work on enumeration problems of these structures by constructive methods. We will mainly concentrate on the following problems: Enumerating major index and amajor index of tableaux of a given shape, the symmetry and unimodality of the resulting major/amajor polynomials, statistics on lattice paths and their relation with Young tableaux in a (k,l)-hook, uniform distribution on lattice paths with restrictions, and enumerations on trees with restriction on the degree of vertices;