Geodesic
Gram matrices and Stirling numbers of a class of diagram algebras,~II
Algebra and discrete mathematics, Tome 25 (2018) no. 2, pp. 215-256

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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.
Keywords: signed partition algebras, algebra of $\mathbb{Z}_2$-relations.
Mots-clés : Gram matrices, partition algebras 
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     author = {N. Karimilla Bi and M. Parvathi},
     title = {Gram matrices and {Stirling} numbers of a class of diagram {algebras,~II}},
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N. Karimilla Bi; M. Parvathi. Gram matrices and Stirling numbers of a class of diagram algebras,~II. Algebra and discrete mathematics, Tome 25 (2018) no. 2, pp. 215-256. http://geodesic.mathdoc.fr/item/ADM_2018_25_2_a4/