Linear Recurrent Double Sequences with Constant Border in M2(F2) are Classified According to Their Geometric Content

Mihai Prunescu
2011 Symmetry  
The author used the automatic proof procedure introduced in [1] and verified that the 4096 homomorphic recurrent double sequences with constant borders defined over Klein's Vierergruppe K and the 4096 linear recurrent double sequences with constant border defined over the matrix ring M 2 (F 2 ) can be also produced by systems of substitutions with finitely many rules. This permits the definition of a sound notion of geometric content for most of these sequences, more exactly for those which are
more » ... not primitive. We group the 4096 many linear recurrent double sequences with constant border I over the ring M 2 (F 2 ) in 90 geometric types. The classification over Klein's Vierergruppe K is not explicitly displayed and consists of the same geometric types like for M 2 (F 2 ), but contains more exceptions. There are a lot of cases of unsymmetric double sequences converging to symmetric geometric contents. We display also geometric types occurring both in a monochromatic and in a dichromatic version.
doi:10.3390/sym3030402 fatcat:sgvp3w5zczeafmajqeflp6unh4