Gram matrices and Stirling numbers of a class of diagram algebras, II
In the paper [6], we introduced Gram matrices for the signed partition algebras, the algebra of \(\mathbb{Z}_2\)-relations and the partition algebras. \((s_1, s_2, r_1, r_2, p_1, p_2)\)-Stirling numbers of the second kind are also introduced and their identities are established. In this paper, we pr...
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| Date: | 2018 |
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| Main Authors: | , |
| 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/1219 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Summary: | In the paper [6], we introduced Gram matrices for the signed partition algebras, the algebra of \(\mathbb{Z}_2\)-relations and the partition algebras. \((s_1, s_2, r_1, r_2, p_1, p_2)\)-Stirling numbers of the second kind are also introduced and their identities are established. In this paper, we prove that the Gram matrix is similar to a matrix which is a direct sum of block submatrices. As a consequence, the semisimplicity of a signed partition algebra is established. |
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