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On positional representation of integer vectors
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NSTL
Elsevier
We show that any m x m matrix Mwith integer entries and det M = Delta not equal 0 can be equipped by a finite digit set D subset of Z(m) such that any integer m-dimensional vector belongs to the set Fin(D)(M) = {Sigma(k epsilon I) M(k)d(k) : theta not equal I finite subsetof Z and d(k) epsilon D for each k epsilon I}subset of boolean OR(k epsilon N) 1/Delta(k) Z(m). We also characterize the matrices M for which the sets Fin(D)(M) and boolean OR(k epsilon N) 1/Delta(k) Z(m) coincide. (C) 2021 Elsevier Inc. All rights reserved.
NSTL
Elsevier
