Sets with two associative operations
By T. Pirashvili. 2003
64 citations recorded by the source corpus.
In this paper we consider duplexes, which are sets with two associative binary operations. Dimonoids in the sense of Loday are examples of duplexes. The set of all permutations carries a structure of a duplex. Our main result asserts that it is a free duplex with an explicitly described set of generators. The proof uses a construction of the free duplex with one generator by planary trees.
Subfields: Algebra and Number Theory, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/c777f4429e7884f4860cc0dc76812ed0a98d0ff9
How researchers see this paper
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In Algebra and Number Theory
- Li Guo
- Kurusch Ebrahimi-Fard
- Jean-Louis Loday
- William F. Keigher
- Yuqun Chen
- Leonid A. Bokut
- Abdenacer Makhlouf
- Donald Yau
In Computational Theory and Mathematics
- Kurusch Ebrahimi-Fard
- Li Guo
- Jean-Louis Loday
- William F. Keigher
- Donald Yau
- Abdenacer Makhlouf
- Jianjun Qiu
- Yuqun Chen
Citations in the corpus
- Generalized bialgebras and triples of operads (2006, background): “The same structure in the category of sets, instead of vector spaces, has been investigated by Teimuraz Pirashvili in [72] under the name duplex.”
- FREE ROTA–BAXTER ALGEBRAS AND ROOTED TREES (2005, background): “So kF with the operations ⊔ and ⋄ forms a 2-associative algebra in the sense of [50, 53].”