2003/01/22 by Teimuraz Pirashvili, Pirashvili, Teimuraz · 1 citation
Computer Science · Mathematics · #05E99 #08B20 #20M05 #Advanced Algebra and Logic #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05E99 #msc:08B20 #msc:20M05
paper · pdf · doi:10.48550/arxiv.math/0301248
arxiv created 2003/01/22 · openalex publication_date 2003/01/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we consider dimonoids, which are sets equipped with two associative binary operations. Dimonoids in the sense of J.-L. Loday are xamples of duplexes. The set of all permutations, gives an example of a duplex which is not a dimonoid. We construct a free duplex generated by a given set via planar trees and then we prove that the set of all permutations form a free duplex on an explicitly described set of generators. We also consider duplexes coming from planar binary trees and vertices of the cubes. We prove that these duplexes are free with one generator in appropriate variety of duplexes.