Geodesic
Gram matrices and Stirling numbers of a class of diagram algebras,~I
Algebra and discrete mathematics, Tome 25 (2018) no. 1, pp. 73-97

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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 for the signed partition algebras, the algebra of $\mathbb{Z}_2$-relations are introduced and their identities are established. Stirling numbers of the second kind for the partition algebras are introduced and their identities are established. 
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     title = {Gram matrices and {Stirling} numbers of a class of diagram {algebras,~I}},
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N. Karimilla Bi; M. Parvathi. Gram matrices and Stirling numbers of a class of diagram algebras,~I. Algebra and discrete mathematics, Tome 25 (2018) no. 1, pp. 73-97. http://geodesic.mathdoc.fr/item/ADM_2018_25_1_a6/