Mixable shuffles, quasi-shuffles and Hopf algebras

By Kurusch Ebrahimi-Fard, Li Guo. 2005

75 citations recorded by the source corpus.

The quasi-shuffle product and mixable shuffle product are both generalizations of the shuffle product and have both been studied quite extensively recently. We relate these two generalizations and realize quasi-shuffle product algebras as subalgebras of mixable shuffle product algebras. As an application, we obtain Hopf algebra structures in free Rota–Baxter algebras.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/c4f89b69fb52a3e62ed279e0785df4dc839646bf

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In Algebra and Number Theory

1. Li Guo
2. Bin Zhang
3. Kurusch Ebrahimi-Fard
4. William F. Keigher
5. Yuqun Chen
6. Leonid A. Bokut
7. Jianjun Qiu
8. Abdenacer Makhlouf

In Discrete Mathematics and Combinatorics

1. Li Guo
2. Bin Zhang
3. Dominique Manchon
4. S. Paycha
5. Kurusch Ebrahimi-Fard

In Geometry and Topology

1. Bin Zhang
2. Li Guo
3. Kurusch Ebrahimi-Fard
4. William F. Keigher
5. Yuqun Chen
6. Leonid A. Bokut
7. Jianjun Qiu
8. Abdenacer Makhlouf

Citations in the corpus

• Embedding of dendriform algebras into Rota-Baxter algebras (2011, unknown): “) can be found [2, 17, 22, 26].”
• Renormalization of multiple zeta values (2006, background): “It is shown [16] to be the same as the mixable shuffle product [26, 27] which is also called overlapping shuffles [28] and generalized shuffles [23], and can be interpreted in terms of Delannoy paths [1, 21, 35].”