This article is cited in 2 papers

Proper cyclic symmetries of multidimensional continued fractions

I. A. Tlyustangelov<sup>ab

a</sup> Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
^b Moscow Center of Fundamental and Applied Mathematics, Moscow, Russia

Abstract: We show that palindromic continued fractions exist in an arbitrary dimension. For dimension $n=4$ we also prove a criterion for an algebraic continued fraction to have a proper cyclic palindromic symmetry. Klein polyhedra are considered as multidimensional generalizations of continued fractions.
Bibliography: 11 titles.

Keywords: Klein polyhedron, cyclic extension.

MSC: 11A55, 11J70

Received: 08.11.2021 and 24.05.2022

DOI: 10.4213/sm9690

 English version: Sbornik: Mathematics, 2022, 213:9, 1290–1317

Bibliographic databases:

• 
• 
• 
• 
•