Geodesic
On an algebraicity theorem of Kontsevich
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) (2012).

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We give in a particular case a combinatorial proof of a recent algebraicity result of Kontsevich; the proof uses generalized one-sided and two-sided Dyck words, or equivalently, excursions and bridges. We indicate a noncommutative version of these notions, which could lead to a full proof. We show also a relation with pointed planar maps. 
@article{DMTCS_2012_special_263_a21,
     author = {Reutenauer, Christophe and Robado, Marco},
     title = {On an algebraicity theorem of {Kontsevich}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)},
     year = {2012},
     doi = {10.46298/dmtcs.3035},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3035/}
}
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Reutenauer, Christophe; Robado, Marco. On an algebraicity theorem of Kontsevich. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) (2012). doi : 10.46298/dmtcs.3035. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3035/

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