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- W2158418060 abstract "Let ${A_k} = { 0,{a_2},{a_3}, ldots ,{a_k}}$ and $B = { 0,{b_2},{b_3}, ldots }$ be sets of nonnegative integers of $k$ elements and infinitely many elements, respectively. Suppose $B$ has asymptotic density $x:d(B) = x$. If, for every integer $n geqq 0$, we can find ${a_i} in {A_k},{b_j} in B$ such that $n = {a_i} + {b_j}$, then we say that ${A_k}$ has a complement of density $leqq x$. Given ${A_k}$ and $x$ there is no known algorithm for determining if such a set $B$ exists. We define regular complement and give an algorithm for determining if $B$ exists when complement is replaced by regular complement. More precisely, given ${A_4}$ and $x = 1/3$ we give an algorithm for determining if ${A_4}$ has a regular complement $B$ with density $leqq 1/3$. We relate this result to the Conjecture. Every ${A_4}$ has a complement of density $leqq 1/3$." @default.
- W2158418060 created "2016-06-24" @default.
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- W2158418060 date "1976-01-01" @default.
- W2158418060 modified "2023-10-18" @default.
- W2158418060 title "An algorithm for complements of finite sets of integers" @default.
- W2158418060 cites W2001168024 @default.
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- W2158418060 doi "https://doi.org/10.1090/s0002-9939-1976-0435023-6" @default.
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