ON ASYMPTOTIC BASES WHICH HAVE DISTINCT SUBSET SUMS
| Autor: | Vinh Hung Nguyen, Sándor Z. Kiss |
|---|---|
| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Bulletin of the Australian Mathematical Society. 104:211-217 |
| ISSN: | 1755-1633 0004-9727 |
| DOI: | 10.1017/s0004972721000174 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|