Geodesic
Some formulas for numbers of restricted words
Journal of integer sequences, Tome 20 (2017) no. 6.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: For an arithmetic function $f_{0}$, we consider the number $c_{m}(n,k)$ of weighted compositions of $n$ into $k$ parts, where the weights are the values of the $(m-1)^{th}$ invert transform of $f_{0}$. We connect $c_{m}(n,k)$ with $c_{1}(n,k)$ via Pascal matrices. We then relate $c_{m}(n,k)$ to the number of certain restricted words over a finite alphabet. In addition, we develop a method which transfers some properties of restricted words over a finite alphabet to words over a larger alphabet.
Classification : 05A10, 11B39
Keywords: binary word, integer composition, restricted word, Pascal matrix 
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     author = {Janji\'c, Milan},
     title = {Some formulas for numbers of restricted words},
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     number = {6},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2017__20_6_a3/}
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Janjić, Milan. Some formulas for numbers of restricted words. Journal of integer sequences, Tome 20 (2017) no. 6. http://geodesic.mathdoc.fr/item/JIS_2017__20_6_a3/