We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
On Abelian 2-avoidable binary patterns.
- Authors
Currie, James; Visentin, Terry
- Abstract
We give the first example of a binary pattern which is Abelian 2-avoidable, but which contains no Abelian fourth power. We introduce a family $$\{f_n\}_{n=1}^\infty$$ of binary morphisms which offer a common generalization of the Fibonacci morphism and the Abelian fourth-power-free morphism of Dekking. We show that the Fibonacci word begins with arbitrarily high Abelian powers, but for n ≥ 2, the fixed point of f n avoids x n+2 in the Abelian sense. The sets of patterns avoided in the Abelian sense by the fixed points of f n and f n+1 are mutually incomparable for n ≥ 2.
- Subjects
COMPUTER programming; MORPHISMS (Mathematics); CATEGORIES (Mathematics); SET theory; ABELIAN functions; COMPUTER algorithms
- Publication
Acta Informatica, 2007, Vol 43, Issue 8, p521
- ISSN
0001-5903
- Publication type
Article
- DOI
10.1007/s00236-006-0030-z