Facet Connectedness of Arithmetic Discrete Hyperplanes with Non-Zero Shift

International audienceWe present a criterion for the arithmetic discrete hyperplane Open image in new window to be facet connected when θ is the connecting thickness Open image in new window . We encode the shift μ in a numeration system associated with the normal vector Open image in new window and we describe an incremental construction of the plane based on this encoding. We deduce a connectedness criterion and we show that when the Fully Subtractive algorithm applied to Open image in new window has a periodic behaviour, the encodings of shifts μ for which the plane is connected may be recognised by a finite state automaton