Mirror substitutions and palindromic sequences

Mirror substitutions and palindromic sequences

By introducing the notion of mirror substitution, we show that, given a substitutive sequence over two letters, it is palindromic (that is, it contains arbitrarily long palindromes) if and only if its language is mirror-invariant (that is, it is closed under the mirror image map). Then we solve a question of Hof, Knill and Simon in the 2-letter case, and also, by constructing a counterexample, ...

Invertible substitutions and Sturmian sequences

It is known on the one hand that a Sturmian sequence can be generated geometrically by the intersections of a straight line with the unit grid in the plane, and on the other hand that fixed points of invertible substitutions are Sturmian. We give a new characterization of invertible substitutions, which allows to determine the straight line which generates the fixed point of a given invertible ...

Bidimensional Sturmian Sequences and Substitutions

Palindromic sequences generated from marked morphisms

Fixed points u = φ(u) of marked and primitive morphisms φ over arbitrary alphabet are considered. We show that if u is palindromic, i.e., its language contains infinitely many palindromes, then some power of φ has a conjugate in class P. This class was introduced by Hof, Knill and Simon (1995) in order to study palindromic morphic words. Our definitions of marked and well-marked morphisms are m...

Comparison of physical and genetic properties of palindromic DNA sequences.

Some viable palindromic DNA sequences were found to cause an increase in the recovery of genetic recombinants. Although these palindromes contained no Chi sites, their presence in cis caused apparent recA+-dependent recombination to increase severalfold. This biological property did not correlate with the physical properties of the palindromes' extrusion of cruciform structures in vitro. Thus, ...