A vertex coloring f of a graph G is nonrepetitive if there are no integer r≥ 1 and a simple
path v1,…, v2r in G such that f (vi)= f (vr+ i) for all i= 1,…, r. This notion is a graph‐theoretic …

There Are Ternary Circular Square-Free Words of Length n for n >= 18 Page 1 There are ternary
circular square-free words of length n for n ≥ 18. James D. Currie ∗ Department of Mathematics …

A sequence S= s1s2… sn is said to be nonrepetitive if no two adjacent blocks of S are the
same. A celebrated 1906 theorem of Thue asserts that there are arbitrarily long nonrepetitive …

Pattern avoidance: themes and variations Page 1 Theoretical Computer Science 339 (2005) 7 –
18 www.elsevier.com/locate/tcs Pattern avoidance: themes and variations James D. Currie ∗,1 …

Internationally recognised researchers look at developing trends in combinatorics with
applications in the study of words and in symbolic dynamics. They explain the important …

Abstract The original Self-Organizing Feature Map (SOFM) has been extended in many
ways to suit different goals and application domains. However, the topologies of the map …

In a recent paper, one of us posed three open problems concerning squarefree arithmetic
progressions in infinite words. In this paper we solve these problems and prove some …

A coloring of the vertices of a graph G is nonrepetitive if there is no even path in G whose
first half looks the same as the second half. This notion arose as an analogue of the famous …

Let G be a graph and let c be a coloring of its edges. If the sequence of colors along a walk
of G is of the form a1,..., an, a1,..., an, the walk is called a square walk. We say that the …

Abstract A sequence $ u= u_ {1} u_ {2}... u_ {n} $ is said to be nonrepetitive if no two
adjacent blocks of $ u $ are exactly the same. For instance, the sequence $ a {\bf bcbc} ba …