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. 
@article{ADM_2016_21_1_a1,
     author = {Eugenija Bondar},
     title = {Classification of $\mathscr{L}$-cross-sections of the finite symmetric semigroup  up to isomorphism},
     journal = {Algebra and discrete mathematics},
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     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2016_21_1_a1/}
}
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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/