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- W3155695687 abstract "Abstract Let k and l be positive integers satisfying $k ge 2, l ge 1$ . A set $mathcal {A}$ of positive integers is an asymptotic basis of order k if every large enough positive integer can be represented as the sum of k terms from $mathcal {A}$ . About 35 years ago, P. Erdős asked: does there exist an asymptotic basis of order k where all the subset sums with at most l terms are pairwise distinct with the exception of a finite number of cases as long as $l le k - 1$ ? We use probabilistic tools to prove the existence of an asymptotic basis of order $2k+1$ for which all the sums of at most k elements are pairwise distinct except for ‘small’ numbers." @default.
- W3155695687 created "2021-04-26" @default.
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- W3155695687 date "2021-04-12" @default.
- W3155695687 modified "2023-10-16" @default.
- W3155695687 title "ON ASYMPTOTIC BASES WHICH HAVE DISTINCT SUBSET SUMS" @default.
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- W3155695687 doi "https://doi.org/10.1017/s0004972721000174" @default.
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