Balanced Simplices
نویسنده
چکیده
An additive cellular automaton is a linear map on the set of infinite multidimensional arrays of elements in a finite cyclic group Z/mZ. In this paper, we consider simplices appearing in the orbits generated from arithmetic arrays by additive cellular automata. We prove that they constitute a source of balanced simplices, that are simplices containing all the elements of Z/mZ with the same multiplicity. For any additive cellular automaton of dimension 1 or higher, the existence of infinitely many balanced simplices of Z/mZ appearing in such orbits is shown, and this, for an infinite number of values m. The special case of the Pascal cellular automata, the cellular automata generating the multidimensional simplices of Pascal, is studied in detail.
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تاریخ انتشار 2014