Symmetries in Generalized Kaprekar’s Routine

Symmetry

Fernando Nuez¹ 

[1] Institute for Conservation and Improvement of Valencian Agrodiversity (COMAV, UPV), Universitat Politècnica de València, 46022 Valencia, Spain;

关键词: number theory;    arithmetic dynamics;    groups;   

DOI  :  10.3390/sym14010037

来源: DOAJ

【 摘 要 】

In this paper, algebraic relations were established that determined the invariance of a transformed number after several transformations. The restrictions that determine the group structure of these relationships were analyzed, as was the case of the Klein group. Parametric $K^r$ functions associated with the existence of cycles were presented, as well as the role of the number of their links in the grouping of numbers in higher-order equivalence classes. For this, we developed a methodology based on binary equivalence relations and the complete parameterization of the Kaprekar routine using Ki functions of parametric transformation.

【 授权许可】

Unknown