Geodesic
Combinatorics of partial wreath power of finite inverse symmetric semigroup $\mathcal{IS}_d$
Algebra and discrete mathematics, no. 1 (2007), pp. 49-60

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We study some combinatorial properties of $\wr_p^k \mathcal{IS}_d$. In particular, we calculate its order, the number of idempotents and the number of $\mathcal D$-classes. For a given based graph $\Gamma\subset T$ we compute the number of elements in its $\mathcal D$-class $D_\Gamma$ and the number of $\mathcal R$- and $\mathcal L$-classes in $D_\Gamma$.
Keywords: Wreath product, finite inverse symmetric semigroup, rooted tree
Mots-clés : partial automorphism. 
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     author = {Yevgeniya Kochubinska},
     title = {Combinatorics of partial wreath power of finite inverse symmetric semigroup $\mathcal{IS}_d$},
     journal = {Algebra and discrete mathematics},
     pages = {49--60},
     publisher = {mathdoc},
     number = {1},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2007_1_a4/}
}
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Yevgeniya Kochubinska. Combinatorics of partial wreath power of finite inverse symmetric semigroup $\mathcal{IS}_d$. Algebra and discrete mathematics, no. 1 (2007), pp. 49-60. http://geodesic.mathdoc.fr/item/ADM_2007_1_a4/