We study formulas for eigenvectors of strongly connected simply laced quivers in terms of eigenvalues. The relation of these formulas to the isomorphism of quivers is investigated.

The paper is a generalization of. For a group H = hA|Oi, conditions for the equality N1 ∩ N2 = [N1, N2] are given in terms of pictures, where Ni is the normal closure of a set R i ⊂ H for i = 1, 2.

For any two positive integers m, n, we denote the graph Km,n ⊙ K1 by G. Ma Ke-Jie proposed a conjecture [9] that pendant edge extension of a complete bipartite graph is a k- graceful graph for k > 2. In this paper we ...

The extensions of hypersubstitutions are mappings on the set of all terms. In the present paper we characterize all hypersubstitutions which provide bijections on the set of all terms. The set of all such hypersubstitutions ...

We give a complete description of the finite posets of width two with the Tits form to be positive. This problem arises in studying the categories of representations of posets of finite type.

We introduce and analyze the following general concept of recurrence. Let G be a group and let X be a G-space with the action G × X −→ X, (g, x) 7−→ gx. For a family F of subset of X and A ∈ F, we denote ∆F(A) = {g ∈ G ...

In this paper we consider the problem on classifying the representations of a pair of posets with involution. We prove that if one of these is a chain of length at least 4 with trivial involution and the other is with ...

It is shown that the set of pairwise non-isomorphic 2-generated simple groups of exponent n (n ≥ 248 and n is odd or divisible by 29) is of cardinality continuum. As a corollary, for any sufficiently large n the set of ...