MATHEMATICA BOHEMICA, Vol. 132, No. 3, pp. 297-323 (2007)

Presentation of the singular part of
the Brauer monoid

Victor Maltcev, Volodymyr Mazorchuk

Victor Maltcev, School of Mathematics and Statistics, St. Andrews University, North Haugh, St. Andrews, Fife KY16 9SS, United Kingdom, e-mail: victor@mcs.st-and.ac.uk; Volodymyr Mazorchuk, Department of Mathematics, Uppsala University, Box 480, SE-75106, Uppsala, Sweden, e-mail: mazor@math.uu.se

Abstract: 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.

Keywords: semigroup, presentation, symmetric group, Brauer monoid

Classification (MSC2000): 20M05, 20M20

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