Geodesic
Immaculate basis of the non-commutative symmetric functions
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) (2013).

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We introduce a new basis of the non-commutative symmetric functions whose elements have Schur functions as their commutative images. Dually, we build a basis of the quasi-symmetric functions which expand positively in the fundamental quasi-symmetric functions and decompose Schur functions according to a signed combinatorial formula. 
@article{DMTCS_2013_special_264_a81,
     author = {Berg, Chris and Bergeron, Nantel and Saliola, Franco and Serrano, Luis and Zabrocki, Mike},
     title = {Immaculate basis of the non-commutative symmetric functions},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)},
     year = {2013},
     doi = {10.46298/dmtcs.12810},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.12810/}
}
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AU  - Bergeron, Nantel
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%V DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
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Berg, Chris; Bergeron, Nantel; Saliola, Franco; Serrano, Luis; Zabrocki, Mike. Immaculate basis of the non-commutative symmetric functions. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) (2013). doi : 10.46298/dmtcs.12810. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.12810/

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