Open AccessCrystal structures and continued fractions
Author(s) -
L V Pekhtereva,
V. A. Seleznëv
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/2099/1/012012
Subject(s) - unimodular matrix , representation (politics) , lattice (music) , morphism , matrix representation , mathematics , crystal structure , gauss , integer (computer science) , matrix (chemical analysis) , crystallography , combinatorics , pure mathematics , physics , computer science , materials science , chemistry , group (periodic table) , programming language , quantum mechanics , politics , political science , acoustics , law , composite material
In this paper, we consider the properties of a flat crystal structure associated with the matrix representation of finite continued fractions generating unimodular morphisms of a flat integer lattice. The used matrix representations of the continued fractions and their properties are obtained in [1]. The constructed model allows us to explain the existing limitations of the sets of Weiss parameters (the rational ratio of the lengths of the edges of the forming cell) of crystals by the Gauss-Kuzmin distribution of natural numbers in the representation of continued fractions.