On Distinct Consecutive Differences
نویسندگان
چکیده
We show that if \(A=\{a_1< a_2< \ldots < a_k\}\) is a set of real numbers such the differences consecutive elements are distinct, then for and finite \(B \subset \mathbb {R}\), $$ |A+B|\gg |A|^{1/2}|B|. $$ The bound tight up to constant.
منابع مشابه
On Distinct Consecutive Differences
We show that if A = {a1, a2, . . . , ak} is a monotone increasing set of numbers, and the differences of the consecutive elements are all distinct, then |A+B| ≥ c|A|1/2|B| for any finite set of numbers B. The bound is tight up to the constant multiplier.
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ژورنال
عنوان ژورنال: Springer proceedings in mathematics & statistics
سال: 2021
ISSN: ['2194-1009', '2194-1017']
DOI: https://doi.org/10.1007/978-3-030-67996-5_24