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Constructing combinatorial operads from monoids
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) Cet article a éte moissonné depuis la source Episciences

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We introduce a functorial construction which, from a monoid, produces a set-operad. We obtain new (symmetric or not) operads as suboperads or quotients of the operad obtained from the additive monoid. These involve various familiar combinatorial objects: parking functions, packed words, planar rooted trees, generalized Dyck paths, Schröder trees, Motzkin paths, integer compositions, directed animals, etc. We also retrieve some known operads: the magmatic operad, the commutative associative operad, and the diassociative operad. 
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     author = {Giraudo, Samuele},
     title = {Constructing combinatorial operads from monoids},
     journal = {Discrete mathematics & theoretical computer science},
     year = {2012},
     volume = {DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)},
     doi = {10.46298/dmtcs.3034},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3034/}
}
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Giraudo, Samuele. Constructing combinatorial operads from monoids. 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.3034

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