Operated semigroups, Motzkin paths and rooted trees
By Li Guo. 2007
119 citations recorded by the source corpus.
Abstract 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.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/16e8fb6ec1dfd29cfd39b16ed3a48ebaa467945d
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In Algebra and Number Theory
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Citations in the corpus
- Matching Rota-Baxter algebras, matching dendriform algebras and matching pre-Lie algebras (2019, unknown): “ RotaBaxter algebra of weight λ by taking Ω to be a singleton. (b) An earlier notion of algebras with multiple Rota-Baxter operators, called a Rota-Baxter family algebra, was defined in [17]. See also [24, 49]. The difference is that there the index set Ω is a semigroup and the Rota-Baxter equation in”
- Grobner-Shirshov Bases for Associative Algebras with Multiple Operators and Free Rota-Baxter Algebras ∗† (2008, methodology): “A free associative algebra with unary operators are constructed by L. Guo [ 32 ].”