Geodesic
Presentation of the singular part of the Brauer monoid
Mathematica Bohemica, Tome 132 (2007) no. 3, pp. 297-323.

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We obtain a presentation for the singular part of the Brauer monoid with respect to an irreducible system of generators consisting of idempotents. As an application of this result we get a new construction of the symmetric group via connected sequences of subsets. Another application describes the lengths of elements in the singular part of the Brauer monoid with respect to the system of generators mentioned above.
DOI : 10.21136/MB.2007.134125
Classification : 20B30, 20M05, 20M20
Keywords: semigroup; presentation; symmetric group; Brauer monoid; irreducible systems of generators; idempotents 
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Maltcev, Victor; Mazorchuk, Volodymyr. Presentation of the singular part of the Brauer monoid. Mathematica Bohemica, Tome 132 (2007) no. 3, pp. 297-323. doi : 10.21136/MB.2007.134125. http://geodesic.mathdoc.fr/articles/10.21136/MB.2007.134125/

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