Geodesic
Classification of $\mathscr{L}$-cross-sections of the finite symmetric semigroup up to isomorphism
Algebra and discrete mathematics, Tome 21 (2016) no. 1, pp. 1-17.

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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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Eugenija Bondar. Classification of $\mathscr{L}$-cross-sections of the finite symmetric semigroup  up to isomorphism. Algebra and discrete mathematics, Tome 21 (2016) no. 1, pp. 1-17. http://geodesic.mathdoc.fr/item/ADM_2016_21_1_a1/

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