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

Eugenija Bondar


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.


symmetric semigroup, cross-section, Green's relations

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