ON ASYMPTOTIC BASES WHICH HAVE DISTINCT SUBSET SUMS

نویسندگان

چکیده

Abstract Let k and l be positive integers satisfying $k \ge 2, 1$ . A set $\mathcal {A}$ of is an asymptotic basis order if every large enough integer can represented as the sum terms from About 35 years ago, P. Erdős asked: does there exist where all subset sums with at most are pairwise distinct exception a finite number cases long $l \le - ? We use probabilistic tools to prove existence $2k+1$ for which elements except ‘small’ numbers.

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ژورنال

عنوان ژورنال: Bulletin of The Australian Mathematical Society

سال: 2021

ISSN: ['0004-9727', '1755-1633']

DOI: https://doi.org/10.1017/s0004972721000174