Gram matrices and Stirling numbers of a class of diagram algebras

Abstract

In this paper, we introduce Gram matrices for

the signed partition algebras, the algebra of Z2-relations and the par- tition algebras. The nondegeneracy and symmetic nature of these

Gram matrices are establised. Also, (s1, s2, r1, r2, p1, p2)-Stirling numbers of the second kind for the signed partition algebras, the algebra of Z2-relations are introduced and their identities are estab- lished. Stirling numbers of the second kind for the partition algebras are introduced and their identities are established.