Displaying similar documents to “A semigroup approach to wreath-product extensions of Solomon's descent algebras.”

A combinatorial proof of a result for permutation pairs

Toufik Mansour, Mark Shattuck (2012)

Open Mathematics

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In this paper, a direct combinatorial proof is given of a result on permutation pairs originally due to Carlitz, Scoville, and Vaughan and later extended. It concerns showing that the series expansion of the reciprocal of a certain multiply exponential generating function has positive integer coefficients. The arguments may then be applied to related problems, one of which concerns the reciprocal of the exponential series for Fibonacci numbers.

Presentation of the singular part of the Brauer monoid

Victor Maltcev, Volodymyr Mazorchuk (2007)

Mathematica Bohemica

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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.