Counting the occurrences of generalized patterns in words generated by a morphism

Details Counting the occurrences of generalized patterns in words generated by a morphism Counting the occurrences of generalized patterns in words generated by a morphism

2002-10-11

arxiv.org/abs/math/0210170v1

Mathematics

Combinatorics

6 pages

Scientific paper

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.

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