We completely determine all commutative semigroup varieties that are cancellable elements of the lattice SEM of all semigroup varieties. In particular, we verify that a commutative semigroup variety is a cancellable element ...

We study asymptotics of the spectral measure of a randomly chosen partial automorphism of a rooted tree. To every partial automorphism x we assign its action matrix Ax. It is shown that the uniform distribution on eigenvalues ...