Shifts of k-nested sequences

Abstract

We introduce a new class of subshifts of sequences, called k-graph shifts, which expresses nested constraints on k symbols instead of on two symbols like for Dyck shifts. These shifts share many properties with Markov-Dyck shifts but are generally not conjugate to them. We prove that they are conjugate to sofic-Dyck shifts. We give a computation of the multivariate zeta function for this class of shifts.

On certain labelled directed graphs of symbolic dynamics

“…8.3. We describe the subshifts, that were introduced by Béal and Heller in [BH,Section 6], within the framework of of section 6 (or sctiom 7). For this purpose let K be a finite nonempty set, and let…”