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Combinatorial proofs of freeness of some P-algebras
Discrete mathematics & theoretical computer science, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015), DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) (2015) Cet article a éte moissonné depuis la source Episciences

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We present new combinatorial methods for solving algebraic problems such as computing the Hilbert series of a free $P$-algebra over one generator, or proving the freeness of a $P$-algebra. In particular, we apply these methods to the cases of dendriform algebras, quadrialgebras and tridendriform algebras, which leads us to prove a conjecture of Aguiar and Loday about the freeness of the quadrialgebra generated by the permutation 12. 
@article{DMTCS_2015_special_285_a58,
     author = {Vong, Vincent},
     title = {Combinatorial proofs of freeness of some {P-algebras}},
     journal = {Discrete mathematics & theoretical computer science},
     year = {2015},
     volume = {DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)},
     doi = {10.46298/dmtcs.2514},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2514/}
}
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Vong, Vincent. Combinatorial proofs of freeness of some P-algebras. Discrete mathematics & theoretical computer science, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015), DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) (2015). doi: 10.46298/dmtcs.2514

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