It is shown that for groups G and H that act faithfully by finite state automorphisms on regular rooted trees their free product G ∗ H admits a faithful action by finite state automorphisms on some regular rooted tree.

We extend the concept of path-cycles, defined in [2], to the semigroup Pn, of all partial maps on Xn = {1, 2, . . . , n}, and show that the classical decomposition of permutations into disjoint cycles can be extended ...

The pair of families of bijective multivariate maps of kind Fn and Fn −1 on affine space Kn over finite commutative ring K given in their standard forms has a nonlinearity gap if the degree of Fn is bounded from above ...

A metric basis S of a graph G is the subset of vertices of minimum cardinality such that all other vertices are uniquely determined by their distances to the vertices in S. The metric dimension of a graph G is the ...

We study twisted conjugacy classes of a family of groups which are called Houghton’s groups Hn (n ∈ N), the group of translations of n rays of discrete points at infinity. We prove that the Houghton’s groups Hn have the ...