Geodesic
Idempotent $\mathcal{D}$-cross-sections of the finite inverse symmetric semigroup $IS_n$
Algebra and discrete mathematics, no. 3 (2008), pp. 84-87.

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We prove that every finite poset can be embedded in some idempotent $\mathcal{D}$-cross-section of the finite inverse symmetric semigroup $\mathcal{IS}_n$.
Keywords: Inverse symmetric semigroup, Green's relations, cross-sections, posets. 
@article{ADM_2008_3_a5,
     author = {Vasyl Pyekhtyeryev},
     title = {Idempotent $\mathcal{D}$-cross-sections of the finite inverse symmetric  semigroup $IS_n$},
     journal = {Algebra and discrete mathematics},
     pages = {84--87},
     publisher = {mathdoc},
     number = {3},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2008_3_a5/}
}
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Vasyl Pyekhtyeryev. Idempotent $\mathcal{D}$-cross-sections of the finite inverse symmetric  semigroup $IS_n$. Algebra and discrete mathematics, no. 3 (2008), pp. 84-87. http://geodesic.mathdoc.fr/item/ADM_2008_3_a5/