Geodesic
Operated semigroups, Motzkin paths and rooted trees
Journal of Algebraic Combinatorics, Tome 29 (2009) no. 1, pp. 35-62.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Combinatorial objects such as rooted trees that carry a recursive structure have found important applications recently in both mathematics and physics. We put such structures in an algebraic framework of operated semigroups. This framework provides the concept of operated semigroups with intuitive and convenient combinatorial descriptions, and at the same time endows the familiar combinatorial objects with a precise algebraic interpretation. As an application, we obtain constructions of free Rota-Baxter algebras in terms of Motzkin paths and rooted trees.
Keywords: keywords operated semigroups, operated algebras, planar rooted trees, Motzkin paths, Dyck paths, Rota-Baxter algebras 
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     author = {Guo, Li},
     title = {Operated semigroups, {Motzkin} paths and rooted trees},
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     url = {http://geodesic.mathdoc.fr/item/JAC_2009__29_1_a4/}
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Guo, Li. Operated semigroups, Motzkin paths and rooted trees. Journal of Algebraic Combinatorics, Tome 29 (2009) no. 1, pp. 35-62. http://geodesic.mathdoc.fr/item/JAC_2009__29_1_a4/