q-对称函数与q-拟对称函数
q-symmetric functions and q-quasisymmetric functions
摘要：
本文构造了Poirier-Schottenauer代数的q-模拟，它与其它q-组合霍普夫代数有着密切的联系.作为应用，我们用它们实现了\cite{EK}中定义的奇Schur函数，自然地得到了\cite{Ell}中涉及的奇Littlewood-Richardson规则.此外，我们构造了奇Schur函数的加细，称为奇拟对称Schur函数，平行于\cite{HLMW1}中的考虑。所有的q-霍普夫代数都给出了相应的\cite{BLL}意义下的q-对偶分次图.
英文摘要：
In this paper, we construct the q-analogue of Poirier-Reutenauer algebras, related deeply with other q-combinatorial Hopf algebras. As an application, we use them to realize the odd Schur functions defined in \cite{EK}, and naturally obtain the odd Littlewood-Richardson rule concerned in \cite{Ell}. Moreover, we construct the refinement of the odd Schur functions, called odd quasisymmetric Schur functions, parallel to the consideration in \cite{HLMW1}. All the q-Hopf algebras we discuss here provide the corresponding q-dual graded graphs in the sense of \cite{BLL}.
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