Reference : Counting the number of non-zero coefficients in rows of generalized Pascal triangles
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/2268/205077
Counting the number of non-zero coefficients in rows of generalized Pascal triangles
English
Leroy, Julien mailto [Université de Liège > Département de mathématique > Mathématiques discrètes >]
Rigo, Michel mailto [Université de Liège > Département de mathématique > Mathématiques discrètes >]
Stipulanti, Manon mailto [Université de Liège > Département de mathématique > Mathématiques discrètes >]
2017
Discrete Mathematics
Elsevier Science
340
862-881
Yes (verified by ORBi)
International
0012-365X
Amsterdam
The Netherlands
[en] Binomial coefficients ; Pascal triangle ; Subwords ; Stern-Brocot tree ; Farey tree ; Trie of sub words
[en] 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))n≥0 counting the number of positive entries on each row. By introducing a convenient tree structure, we provide a recurrence relation for (S(n))n≥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.
Researchers ; Professionals ; Students
http://hdl.handle.net/2268/205077
10.1016/j.disc.2017.01.003

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