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Finite Representability of Integers as $2$-Sums | | Anant Godbole
; Zach Higgins
; Zoe Koch
; | | Date: |
15 May 2017 | | Abstract: | A set $mathcal{A}$ is said to be an additive $h$-basis if each element in
${0,1,ldots,hn}$ can be written as an $h$-sum of elements of $mathcal{A}$
in {it at least} one way. We seek multiple representations as $h$-sums, and,
in this paper we make a start by restricting ourselves to $h=2$. We say that
$mathcal{A}$ is said to be a truncated $(alpha,2,g)$ additive basis if each
$jin[alpha n, (2-alpha)n]$ can be represented as a $2$-sum of elements of
$mathcal{A}$ in at least $g$ ways. In this paper, we provide sharp asymptotics
for the event that a randomly selected set is a truncated $(alpha,2,g)$
additive basis with high or low probability. | | Source: | arXiv, 1705.5198 | | Services: | Forum | Review | PDF | Favorites | |
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