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

• Datum: 2018
• 1. Verfasser: Kochubinska, Yevgeniya
• Format: Artikel
• Sprache: English
• Veröffentlicht: Lugansk National Taras Shevchenko University 2018
• Schlagworte: Wreath product; finite inverse symmetric semigroup; rooted tree; partial automorphism; 20M18; 20M20; 05C05
• Online Zugang: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/834
• Назва журналу: Algebra and Discrete Mathematics

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...