Avoiding Squares and Overlaps Over the Natural Numbers

Details Avoiding Squares and Overlaps Over the Natural Numbers Avoiding Squares and Overlaps Over the Natural Numbers

2009-01-12

arxiv.org/abs/0901.1397v1

Mathematics

Combinatorics

16 pages, 2 tables

Scientific paper

We consider avoiding squares and overlaps over the natural numbers, using a greedy algorithm that chooses the least possible integer at each step; the word generated is lexicographically least among all such infinite words. In the case of avoiding squares, the word is 01020103..., the familiar ruler function, and is generated by iterating a uniform morphism. The case of overlaps is more challenging. We give an explicitly-defined morphism phi : N* -> N* that generates the lexicographically least infinite overlap-free word by iteration. Furthermore, we show that for all h,k in N with h <= k, the word phi^{k-h}(h) is the lexicographically least overlap-free word starting with the letter h and ending with the letter k, and give some of its symmetry properties.

Affiliated with

Also associated with

No associations

Rating

Avoiding Squares and Overlaps Over the Natural Numbers does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Avoiding Squares and Overlaps Over the Natural Numbers, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Avoiding Squares and Overlaps Over the Natural Numbers will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-531897