Geodesic
Primitive orthogonal idempotents for R-trivial monoids
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) (2011).

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We construct a recursive formula for a complete system of primitive orthogonal idempotents for any R-trivial monoid. This uses the newly proved equivalence between the notions of R-trivial monoid and weakly ordered monoid. 
@article{DMTCS_2011_special_260_a9,
     author = {Berg, Chris and Bergeron, Nantel and Bhargava, Sandeep and Saliola, Franco},
     title = {Primitive orthogonal idempotents for {R-trivial} monoids},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)},
     year = {2011},
     doi = {10.46298/dmtcs.2896},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2896/}
}
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Berg, Chris; Bergeron, Nantel; Bhargava, Sandeep; Saliola, Franco. Primitive orthogonal idempotents for R-trivial monoids. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) (2011). doi : 10.46298/dmtcs.2896. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2896/

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