Geodesic
PreLie-decorated hypertrees
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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Weighted hypertrees have been used by C. Jensen, J. McCammond, and J. Meier to compute some Euler characteristics in group theory. We link them to decorated hypertrees and 2-coloured rooted trees. After the enumeration of pointed and non-pointed types of decorated hypertrees, we compute the character for the action of the symmetric group on these hypertrees. 
@article{DMTCS_2013_special_264_a96,
     author = {Oger, B\'er\'enice},
     title = {PreLie-decorated hypertrees},
     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.12825},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.12825/}
}
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Oger, Bérénice. PreLie-decorated hypertrees. 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.12825. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.12825/

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