Geodesic
$\mathcal{H}$--,$\mathcal{R}$-- and $\mathcal{L}$--cross-sections of the infinite symmetric inverse semigroup $IS_X$
Algebra and discrete mathematics, no. 1 (2005), pp. 92-104.

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All $\mathcal{H}$–,$\mathcal{R}$– and $\mathcal{L}$–cross-sections of the infinite symmetric inverse semigroup $IS_X$ are described.
Keywords: Symmetric inverse semigroup, Green relations, cross-sections. 
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     author = {Vasyl Pyekhtyeryev},
     title = {$\mathcal{H}$--,$\mathcal{R}$-- and $\mathcal{L}$--cross-sections of the infinite symmetric inverse semigroup $IS_X$},
     journal = {Algebra and discrete mathematics},
     pages = {92--104},
     publisher = {mathdoc},
     number = {1},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2005_1_a8/}
}
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Vasyl Pyekhtyeryev. $\mathcal{H}$--,$\mathcal{R}$-- and $\mathcal{L}$--cross-sections of the infinite symmetric inverse semigroup $IS_X$. Algebra and discrete mathematics, no. 1 (2005), pp. 92-104. http://geodesic.mathdoc.fr/item/ADM_2005_1_a8/