A Disturbing Combination of Geometrical and Modular Rotations in the World of Arithmetic

Khaled Ben Letaïef (1)

1 ISAE-SUPAERO - Institut Supérieur de l'Aéronautique et de l'Espace

In previous papers [1] [2], we have examined two types of 'rotations' in associated Stirling numbers of first and second kind at any order r, respectively : 1. Geometrical rotations, which helped to compact all those Stirling numbers in an arithmeti-cal triangle's structure. 2. Modular rotations which determined their arithmetical properties using angles depending on r. Those different types of rotations could be used independently from each other : each paper was devoted to one of them. In this article, we are going to use both rotations in order to obtain new results directly applicable to associated Stirling numbers as we find them written in the scientific literature, i.e. in "elastic stair steps", not in arithmetical triangles.

Mots clés: Number Theory; Associated Stirling Numbers; Modular Rotations; Arithmetical; Triangle; AMS Classification : 11B73; 05A18

Domaines: Combinatoire [math.CO]; Théorie des nombres [math.NT]

Khaled Ben Letaïef. A Disturbing Combination of Geometrical and Modular Rotations in the World of Arithmetic. 2017. ⟨hal-01568068⟩