Shuffle quadri-algebra and concatenation

Dominique Manchon (1) , Mohamed Belhaj (2)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 ISIMG - institut supérieur d'informatique et de multinedia de Gabes

In this article, we study the shuffle quadri-algebra H. We prove the existence of some relations between quadri-algebra laws which constitute shuffle product, the concatenation product and the deconcatenation coproduct. We also show that the underlying shuffle algebra has two module-algebra structures on itself.

Mots clés: quadri-algebra; dendriform algebra; shuffle; concatenation; module-algebra

Domaines: Mathématiques [math]; Combinatoire [math.CO]

Dominique Manchon, Mohamed Belhaj. Shuffle quadri-algebra and concatenation. F. Chapoton, F. Fauvet, Cl. Malvenuto, J.-Y. Thibon. Algebraic Combinatorics, Resurgence, Moulds and Applications (CARMA), Jun 2017, Marseille, France. 31, European Mathematical Society Publishing House, pp.1-27, 2020, IRMA Lectures in Mathematics and Theoretical Physics, ⟨10.4171/204-1/1⟩. ⟨hal-02404122⟩