q-symmetric functions and q-quasisymmetric functions

2013/06/02 by Yunnan Li, Li, Yunnan
Chemistry · Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Molecular spectroscopy and chirality #math.QA

paper · pdf · doi:10.48550/arxiv.1306.0224

pages 36

arxiv created 2013/06/05 · arxiv updated 2013/06/06

Abstract

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 \citeEK, and naturally obtain the odd Littlewood-Richardson rule concerned in \citeEll. Moreover, we construct the refinement of the odd Schur functions, called odd quasisymmetric Schur functions, parallel to the consideration in \citeHLMW1. All the q-Hopf algebras we discuss here provide the corresponding q-dual graded graphs in the sense of \citeBLL.

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