Let A = (aij) be an integral matrix. We say that A is (0, 1, 2)-matrix if aij 2 {0, 1, 2}. There exists the Gorenstein (0, 1, 2)-matrix for any permutation on the set {1, . . . , n} with- out fixed elements. For every ...

In the paper [6], we introduced Gram matrices for the signed partition algebras, the algebra of Z2-relations and the partition algebras. (s1, s2, r1, r2, p1, p2)-Stirling numbers of the second kind are also introduced ...

Using the (universal) Theorem for the integer partitions and the q-binomial Theorem, we give arithmetical and combinatorial identities for the complete Bell polynomials as generating functions for the number of partitions ...

We consider the algebras ei (Q)ei, where (Q) is the deformed preprojective algebra of weight and i is some vertex of Q, in the case where Q is an extended Dynkin diagram and lies on the hyperplane orthogonal to the ...

V.I. Arnold gave a miniversal deformation of matrices of linear operators; that is, a simple canonical form, to which not only a given square matrix A, but also the family of all matrices close to A, can be reduced by ...