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.
@article{bwmeta1.element.doi-10_2478_BF02476006,
author = {Teimuraz Pirashvili},
title = {Sets with two associative operations},
journal = {Open Mathematics},
volume = {1},
year = {2003},
pages = {169-183},
zbl = {1032.16032},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02476006}
}
Teimuraz Pirashvili. Sets with two associative operations. Open Mathematics, Tome 1 (2003) pp. 169-183. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02476006/
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