Gram matrices and Stirling numbers of a class of diagram algebras, I

• Date: 2018
• Main Authors: Karimilla Bi, N., Parvathi, M.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: Gram matrices; partition algebras; signed partition algebras and the algebra of \(\mathbb{Z}_2\)-relations; 16Z05
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/36
• Journal Title: Algebra and Discrete Mathematics

In this paper, we introduce Gram matrices for the signed partition algebras, the algebra of \(\mathbb{Z}_2\)-relations and the partition algebras. The nondegeneracy and symmetic nature of these Gram matrices are establised. Also, \((s_1, s_2, r_1, r_2, p_1, p_2)\)-Stirling numbers of the second kind...