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Typed Angularly Decorated Planar Rooted Trees and Ω-Rota-Baxter Algebras

Author

Listed:
  • Yi Zhang

    (School of Mathematics and Statistics, Nanjing University of Information Science & Technology, Nanjing 210044, China)

  • Xiaosong Peng

    (School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China)

  • Yuanyuan Zhang

    (School of Mathematics and Statistics, Henan University, Kaifeng 475004, China)

Abstract

As a generalization of Rota–Baxter algebras, the concept of an Ω -Rota–Baxter could also be regarded as an algebraic abstraction of the integral analysis. In this paper, we introduce the concept of an Ω -dendriform algebra and show the relationship between Ω -Rota–Baxter algebras and Ω -dendriform algebras. Then, we provide a multiplication recursion definition of typed, angularly decorated rooted trees. Finally, we construct the free Ω -Rota–Baxter algebra by typed, angularly decorated rooted trees.

Suggested Citation

  • Yi Zhang & Xiaosong Peng & Yuanyuan Zhang, 2022. "Typed Angularly Decorated Planar Rooted Trees and Ω-Rota-Baxter Algebras," Mathematics, MDPI, vol. 10(2), pages 1-15, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:2:p:190-:d:720221
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