On Sums of Large Sets of Integers
نویسندگان
چکیده
منابع مشابه
On Arithmetic Progressions in Sums of Sets of Integers
3 Proof of Theorem 1 9 3.1 Estimation of the g1 term. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.2 Estimation of the g3 term. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.3 Estimation of the g2 term. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.4 Putting everything together. . . . . . . . . . . . . . . . . . . . . ....
متن کاملA Construction for Sets of Integers with Distinct Subset Sums
A set S of positive integers has distinct subset sums if there are 2|S| distinct elements of the set {∑ x∈X x : X ⊂ S } . Let f(n) = min{maxS : |S| = n and S has distinct subset sums}. Erdős conjectured f(n) ≥ c2n for some constant c. We give a construction that yields f(n) < 0.22002 · 2n for n sufficiently large. This now stands as the best known upper bound on f(n).
متن کاملBalanced Subset Sums in Dense Sets of Integers
Let 1 ≤ a1 < a2 < · · · < an ≤ 2n − 2 denote integers. Assuming that n is large enough, we prove that there exist ε1, . . . , εn ∈ {−1,+1} such that |ε1 + · · ·+εn| ≤ 1 and |ε1a1+ · · ·+εnan| ≤ 1. This result is sharp, and in turn it confirms a conjecture of Lev. We also prove that when n is even, every integer in a large interval centered at (a1 + a2 + · · · + an)/2 can be represented as the s...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1964
ISSN: 0002-9947
DOI: 10.2307/1993687