Flag-transitivity and primitivity

On primitivity and reduction for flag-transitive symmetric designs

We present some results on flag-transitive symmetric designs. First we see what conditions are necessary for a symmetric design to admit an imprimitive, flag-transitive automorphism group. Then we move on to study the possibilities for a primitive, flag-transitive automorphism group, and prove that for λ ≤ 3, the group must be affine or almost simple, and finally we analyse the case in which a ...

Topological Transitivity and Strong Transitivity

We discuss the relation between (topological) transitivity and strong transitivity of dynamical systems. We show that a transitive and open self-map of a compact metric space satisfying a certain expanding condition is strongly transitive. We also prove a couple of results for interval maps; for example it is shown that a transitive piecewise monotone interval map is strongly transitive.

Morphic Primitivity and Alphabet Reductions

An alphabet reduction is a 1-uniform morphism that maps a word to an image that contains a smaller number of different letters. In the present paper we investigate the effect of alphabet reductions on morphically primitive words, i. e., words that are not a fixed point of a nontrivial morphism. Our first main result answers a question on the existence of unambiguous alphabet reductions for such...

Word insertions and primitivity ∗

In this paper we consider relations between the operation of word insertion and primitivity. A necessary and sufficient condition under which the insertion u ← u of the word u into itself has maximum cardinality is obtained. The notion of insertion sequence is introduced and sufficient conditions under which an insertion sequence is a special type of language (regular, context-free, biprefix co...

Primitivity, freeness, norm and trace