q-symmetric functions and q-quasisymmetric functions

Original · EN

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 EK, and naturally obtain the odd Littlewood-Richardson rule concerned in Ell. Moreover, we construct the refinement of the odd Schur functions, called odd quasisymmetric Schur functions, parallel to the consideration in HLMW1. All the q-Hopf algebras we discuss here provide the corresponding q-dual graded graphs in the sense of BLL.