This article is cited in 4 papers

RESEARCH ARTICLE

Combinatorics of partial wreath power of finite inverse symmetric semigroup $\mathcal{IS}_d$

Yevgeniya Kochubinska

Department of Mechanics and Mathematics, Kyiv Taras Shevchenko University, 64, Volodymyrska st., 01033, Kyiv, Ukraine

Abstract: 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, partial automorphism.

MSC: 20M18, 20M20, 05C05

Received: 14.06.2005
Revised: 30.05.2007

Language: English

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