For bipermutive CA of diameter d generating Latin squares of order 2^{d-1}, the main diagonal is a transversal exactly when the local rule induces an invertible periodic-boundary CA on d-1 cells; exhaustive search shows d=6 is the smallest such diameter for nonlinear rules.
Title resolution pending
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
fields
cs.FL 1years
2026 1verdicts
ACCEPT 1representative citing papers
citing papers explorer
-
On the transversals of Latin squares generated by nonlinear bipermutive cellular automata
For bipermutive CA of diameter d generating Latin squares of order 2^{d-1}, the main diagonal is a transversal exactly when the local rule induces an invertible periodic-boundary CA on d-1 cells; exhaustive search shows d=6 is the smallest such diameter for nonlinear rules.