SOME COMBINATORIAL PROPERTIES OF ARSHON SEQUENCES OF ARBITRARY ORDERS

Abstract

Let [Formula: see text] be the Arshon sequence of order m and let [Formula: see text] be the formal language consisting of all finite subwords of [Formula: see text]. In this paper, we (1) show that the avoidability bound for [Formula: see text] is [Formula: see text], (2) characterize the syntactic congruence of [Formula: see text] as a Rees congruence, thus generalizing the results of Klepinin and Sukhanov [On combinatorial properties of the Arshon sequence, Discrete Appl. Math.114(1–3) (2001) 155–169], (3) show that the isoperimetric profile of [Formula: see text] is a constant.