On the Number of Bh -Sets
نویسندگان
چکیده
A set A of positive integers is a Bh-set if all the sums of the form a1+ · · ·+ah, with a1, . . . , ah ∈ A and a1 ≤ · · · ≤ ah, are distinct. We provide asymptotic bounds for the number of Bh-sets of a given cardinality contained in the interval [n] = {1, . . . , n}. As a consequence of our results, we address a problem of Cameron and Erdős (1990) in the context of Bh-sets. We also use these results to estimate the maximum size of a Bh-set contained in a typical (random) subset of [n] with a given cardinality.
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ورودعنوان ژورنال:
- Combinatorics, Probability & Computing
دوره 25 شماره
صفحات -
تاریخ انتشار 2016