Basises of integers under the multiplace shift operations
Matematičeskie voprosy kriptografii, Tome 2 (2011) no. 1, pp. 29-73
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A notion of $(k,m)$-basis of $\mathbb Z$ is defined for integers $k,m$ ($0$, $(k,m)=\nobreakspace1$). Its definition uses an extension operation: a subset $U\subset\mathbb Z$ may be extended to $U\cup\{i,i+k,i+m\}$ if $|U\cap\{i,i+k,i+m\}|=2$ for some $i\in\mathbb Z$. A minimal subset $S\subset\mathbb Z$ is a $(m,k)$-basis if each $z\in\mathbb Z$ belongs to an extension of $S$ obtained by several extension operations. A structure of $(m,k)$-basises is investigated, precise bounds for the number of their elements are obtained.
@article{MVK_2011_2_1_a1,
author = {F. M. Malyshev},
title = {Basises of integers under the multiplace shift operations},
journal = {Matemati\v{c}eskie voprosy kriptografii},
pages = {29--73},
year = {2011},
volume = {2},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MVK_2011_2_1_a1/}
}
F. M. Malyshev. Basises of integers under the multiplace shift operations. Matematičeskie voprosy kriptografii, Tome 2 (2011) no. 1, pp. 29-73. http://geodesic.mathdoc.fr/item/MVK_2011_2_1_a1/
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