Combinatorics of partial wreath power of finite inverse symmetric semigroup \(\mathcal{IS}_d\)
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...
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| Date: | 2018 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2018
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/834 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Summary: | 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 \(D_\Gamma\). |
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