English

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

R2 v1 2026-06-21T22:59:28.391Z