Simple permutations are the building blocks of permutation classes. As such, classes with only finitely many simple permutations, e.g., the class of 132-avoiding permutations, have nice properties. To name three: these classes have algebraic generating functions (as established by Albert and Atkinson [1]; see Brignall, Huczynska, and Vatter [9] for extensions), are partially well-ordered (see t...

Abstract We build on the description of left congruences an inverse semigroup in terms kernel and trace due to Petrich Rankin. The notion for a congruence is developed. Various properties are discussed, particular that full subsemigroup both maps onto $$\cap $$ ? -homomorphisms. It shown determined by its ker...

Abstract. In this paper we investigate multifractal decompositions based on values of Birkhoff averages of functions from a class of symbolically continuous functions. This will be done for an expanding interval map with infinitely many branches and is a generalisation of previous work for expanding maps with finitely many branches. We show that there are substantial differences between this ca...

This paper continues our investigation of the dynamics families transcendental meromorphic functions with finitely many singular values all which are finite. Here we look at a generalization family polynomials $P_a(z)=z^{d-1}(z- \frac{da}{(d-1)})$, $f_{\lambda}=\lambda \tan^p z^q$. These have super-attractive fixed point, and, depending on $p$, one or two asymptotic values. Although dynamical p...