Standard 2D Crystalline Patterns and Rational Points in Complex Quadrics
Combinatorics
2013-01-08 v2 Algebraic Geometry
Abstract
A certain Diophantine problem and 2D crystallography are linked through the notion of standard realizations which was introduced originally in the study of random walks. In the discussion, a complex projective quadric defined over Q is associated with a finite graph. "Rational points" on this quadric turns out to be related to standard realizations of 2D crystal structures.
Keywords
Cite
@article{arxiv.1212.5755,
title = {Standard 2D Crystalline Patterns and Rational Points in Complex Quadrics},
author = {Toshikazu Sunada},
journal= {arXiv preprint arXiv:1212.5755},
year = {2013}
}
Comments
18 pages, 8 figures