Counting the occurrences of generalized patterns in words generated by a morphism
Combinatorics
2007-05-23 v1
Abstract
We count the number of occurrences of certain patterns in given words. We choose these words to be the set of all finite approximations of a sequence generated by a morphism with certain restrictions. The patterns in our considerations are either classical patterns 1-2, 2-1, 1-1-...-1, or arbitrary generalized patterns without internal dashes, in which repetitions of letters are allowed. In particular, we find the number of occurrences of the patterns 1-2, 2-1, 12, 21, 123 and 1-1-...-1 in the words obtained by iterations of the morphism 1->123, 2->13, 3->2, which is a classical example of a morphism generating a nonrepetitive sequence.
Keywords
Cite
@article{arxiv.math/0210170,
title = {Counting the occurrences of generalized patterns in words generated by a morphism},
author = {S. Kitaev and T. Mansour},
journal= {arXiv preprint arXiv:math/0210170},
year = {2007}
}
Comments
6 pages