On \((2,3)\)-simultaneous number systems over the Eisenstein lattice

Abstract. Various authors analysed simultaneous number systems over different lattices. This paper presents additional characterisations on number expansions over the ``triple'' Eisenstein lattice. The main objective is determining a small and enumerable set (so-called testing set), including the periodic points. The algorithmic exploration of these systems poses a significant challenge due to the substantial increase in the size of the digit set and the testing set, even for small parameters. Efficient algorithms are introduced to address the classification problem, and finally, we offer an algorithm for computing the last digit deletion function without storing it.