Classification of \(\mathscr{L}\)-cross-sections of the finite symmetric semigroup up to isomorphism

Eugenija Bondar

Abstract


Let \(\mathscr{T}_n\) be the symmetric semigroup of full transformations on a finite set with \(n\) elements. In the paper we give a counting formula for the number of \(\mathscr{L}\)-cross-sections of \(\mathscr{T}_n\) and classify all
\(\mathscr{L}\)-cross-sections of \(\mathscr{T}_n\) up to isomorphism.


Keywords


symmetric semigroup, cross-section, Green's relations

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References


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E. Bondar, emph{$mathscr{L}$-cross-sections of the finite symmetric semigroup}, Algebra discrete math., Vol.18, N.textbf{1}, 2014, 27--41.


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