Characterization of coincidence site lattices of oblique planar lattices
Marco Antonio Rodr\'iguez-Andrade, Gerardo Arag\'on-Gonz\'alez and, Jos\'e Luis Arag\'on Vera
TL;DR
This paper algebraically characterizes coincidence site lattices of oblique planar lattices using the Cartan-Dieudonné theorem, with detailed analysis of rectangular lattices to understand the oblique case.
Contribution
It introduces an algebraic framework for characterizing coincidence site lattices of oblique lattices using reflections and the Cartan-Dieudonné theorem.
Findings
Detailed characterization of rectangular lattices
Extension to oblique lattices via rectangular case
Use of orthogonal transformations and reflections
Abstract
Coincidence site lattices of oblique planar lattices are algebraically characterized using as basic tool the Cartan-Dieudonn\'e theorem, that is, the decomposition of an orthogonal transformation as a product of reflections. The case of rectangular lattices is worked out in detail. We use the rectangular lattices for obtain the characterization of the corresponding obliques.
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Taxonomy
TopicsMathematics and Applications · graph theory and CDMA systems · Advanced Topics in Algebra