Operated semigroups, Motzkin paths and rooted trees

Details Operated semigroups, Motzkin paths and rooted trees Operated semigroups, Motzkin paths and rooted trees

2007-10-02

arxiv.org/abs/0710.0429v1

Mathematics

Rings and Algebras

28 pages

Scientific paper

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.

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