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- W3133672778 abstract "We show that any $mtimes m$ matrix $M$ with integer entries and $det M =Delta neq 0$ can be equipped by a finite digit set $mathcal{D}subsetmathbb{Z}^m$ such that any integer $m$-dimensional vector belongs to the set $$ {rm Fin}_{mathcal{D}}(M)= Bigl{sum_{kin I}M^k {d}_k : emptysetneq I text{ finite subset of } mathbb{Z} text{ and } {d}_k in mathcal{D} text{ for each } k in IBigr} subset bigcuplimits_{kin mathbb{N}} frac{1}{Delta^k}mathbb{Z}^{m} ,. $$ We also characterize the matrices $M$ for which the sets $ {rm Fin}_{mathcal{D}}(M)$ and $ bigcuplimits_{kin mathbb{N}} frac{1}{Delta^k}mathbb{Z}^{m}$ coincide." @default.
- W3133672778 created "2021-03-15" @default.
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- W3133672778 date "2021-03-03" @default.
- W3133672778 modified "2023-09-27" @default.
- W3133672778 title "On positional representation of integer vectors" @default.
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