Geodesic
Quasisymmetric Schur functions
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008) (2008).

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We introduce a new basis for the algebra of quasisymmetric functions that naturally partitions Schur functions, called quasisymmetric Schur functions. We describe their expansion in terms of fundamental quasisymmetric functions and determine when a quasisymmetric Schur function is equal to a fundamental quasisymmetric function. We conclude by describing a Pieri rule for quasisymmetric Schur functions that naturally generalizes the Pieri rule for Schur functions. 
@article{DMTCS_2008_special_255_a13,
     author = {Haglund, James and Mason, Sarah and Luoto, Kurt and van Willigenburg, Steph},
     title = {Quasisymmetric {Schur} functions},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008)},
     year = {2008},
     doi = {10.46298/dmtcs.3605},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3605/}
}
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%D 2008
%V DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008)
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Haglund, James; Mason, Sarah; Luoto, Kurt; van Willigenburg, Steph. Quasisymmetric Schur functions. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008) (2008). doi : 10.46298/dmtcs.3605. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3605/

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