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Presentation of the singular part of the Brauer monoid

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.

preprint2006arXivOpen access
Victor MaltcevVolodymyr Mazorchuk
math.GR
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Victor MaltcevVolodymyr Mazorchuk

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