Reference : Convergence of Pascal-Like Triangles in Parry–Bertrand Numeration Systems
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Convergence of Pascal-Like Triangles in Parry–Bertrand Numeration Systems
Stipulanti, Manon mailto [Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes >]
Theoretical Computer Science
Yes (verified by ORBi)
[en] Binomial coefficients ; Words ; Pascal triangles ; Parry numbers ; Bertrand numeration systems
[en] We pursue the investigation of generalizations of the Pascal triangle based on binomial coefficients
of finite words. These coefficients count the number of times a finite word appears as a subsequence of another finite word. The finite words occurring in this paper belong to the language of a Parry numeration system satisfying the Bertrand property, i.e., we can add or remove trailing zeroes to valid representations. It is a folklore fact that the Sierpiński gasket is the limit set, for the Hausdorff distance, of a convergent sequence of normalized compact blocks extracted from the classical Pascal triangle modulo 2. In a similar way, we describe and study the subset of [0, 1] × [0, 1] associated with the latter generalization of the Pascal triangle modulo a prime number.
Fonds pour la formation à la Recherche dans l'Industrie et dans l'Agriculture (Communauté française de Belgique) - FRIA
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