An atomic monoid $M$ is called length-factorial if for every non-invertible element $x \in M$, no two distinct factorizations of $x$ into irreducibles have the same length (i.e., number irreducible factors, counting repetitions). The notion length-factoriality was introduced by J. Coykendall and W. Smith in 2011 under term 'other-half-factoriality': they used to provide a characterization uniqu...

We review notions of small sets, φ-irreducibility, etc., and present a simple proof of asymptotic convergence of general state space Markov chains to their stationary distributions.

In an analogy with the Galois homothety property for torsion points of abelian varieties that was used in proof Mordell–Lang conjecture, we describe a correspondence between action group and dynamical rational map. For nonlinear polynomials coefficients, irreducibility associated dynatomic polynomial serves as convenient criterion, although also verify occurs several cases when is reducible. Th...

The purpose of this article is twofold. On one hand, we reveal the equivalence shift finite type between a one-sided X and its associated hom tree-shift TX, as well in sofic shift. other investigate interrelationship among comparable mixing properties on tree-shifts those multidimensional spaces. They include irreducibility, topologically mixing, block gluing, strong all which are defined spiri...