Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5776972 | Discrete Mathematics | 2017 | 20 Pages |
Abstract
This paper is about counting the number of distinct (scattered) subwords occurring in a given word. More precisely, we consider the generalization of the Pascal triangle to binomial coefficients of words and the sequence (S(n))nâ¥0 counting the number of positive entries on each row. By introducing a convenient tree structure, we provide a recurrence relation for (S(n))nâ¥0. This leads to a connection with the 2-regular Stern-Brocot sequence and the sequence of denominators occurring in the Farey tree. Then we extend our construction to the Zeckendorf numeration system based on the Fibonacci sequence. Again our tree structure permits us to obtain recurrence relations for and the F-regularity of the corresponding sequence.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Julien Leroy, Michel Rigo, Manon Stipulanti,