Typed Angularly Decorated Planar Rooted Trees and Ω-Rota-Baxter Algebras - Yi Zhang; Xiaosong Peng; Yuanyuan Zhang (Mathematics, 2022)
As a generalization of Rota–Baxter algebras, the concept of an <semantics>Ω</semantics>-Rota–Baxter could also be regarded as an algebraic abstraction of the integral analysis. In this paper, we introduce the concept of an <semantics>Ω</semantics>-dendriform algebra and show the relationship between <semantics>Ω</semantics>-Rota–Baxter algebras and <semantics>Ω</semantics>-dendriform algebras. Then, we provide a multiplication recursion definition of typed, angularly decorated rooted trees. Finally, we construct the free <semantics>Ω</semantics>-Rota–Baxter algebra by typed, angularly decorated rooted trees.