拟对称函数作为对称函数的延伸，最早由美国科学院院士Richard Stanley在1971年引入，直至1983年才由Ira Gessel教授给出其正式定义。迄今拟对称函数已发展为组合数学的一个重要研究对象，是多个数学领域的一个强有力工具，在计数组合学、对称函数、表示论、离散几何等领域具有广泛应用，其重要性正日益凸显。.本项目旨在从组合的角度研究拟对称函数代数的一组重要的基-拟对称Schur函数。通过探讨拟对称Schur函数与各类型的杨表等组合对象之间的内在联系，研究拟对称Schur函数的一些组合性质，包括三类重要的行列式公式及Murnaghan-Nakayama法则。同时，在更广的一类拟对称函数-斜拟对称Schur函数上研究上述组合性质及另外一些组合性质的模拟。.　　本项目的研究成果将丰富拟对称函数理论，加深理解杨表这一组合对象，并为拟对称函数在其他数学领域的应用提供更多理论支持。

Quasisymmetric functions are extensions of symmetric functions, which were first used around 1970 by Professor Richard Stanley, a member of the US National Academy of Sciences. It was not until 1983 that quasisymmetric functions were formally defined by Professor Ira Gessel. Quasisymmetric functions have developed into an important research object in combinatorics today, they are a powerful tool in many areas of mathematics with extensive applications in enumerative combinatorics, symmetric functions, representation theory, discrete geometry, etc. Now they are becoming of comparable importance..The goal of this project is to investigate an important basis of the algebra of quasisymmetric functions, called quasisymmetric Schur functions, from combinatorial perspective. By exploring the relation between quasisymmetric Schur functions and some combinatorial objects such as Young tableaux of various types, we will discuss some combinatorial properties of quasisymmetric Schur functions, including three important determinantal formulae for quasisymmetric Schur functions and the Murnaghan-Nakayama rule. Furthermore, we will investigate the skew quasisymmetric Schur function analogues of these quasisymmetric Schur function properties and some other combinatorial properties..The results of this research will enrich the theory of quasisymmetric functions, and enhance the understanding of the combinatorial object called Young tableaux. Moreover, it will provide more theoretical supports for the application of quasisymmetric functions in other areas of mathematics.