On consecutive subset sums
نویسندگان
چکیده
منابع مشابه
Subset Sums
IAl > ((l/k) + E)n then there is a subset B L A such that 0 < 1 BI 0, let snd(nt) denote the smallest integer that does not divide PI. We prove that for every I-: > 0 there is a constant c = ~(8:) z I, such that for every n > 0 and every rn, n ' +' 6 WI < n'llog'n...
متن کاملSums of Consecutive Integers
Wai Yan Pong ([email protected]) received his B.Sc. from the Chinese University of Hong Kong and his M.Sc. and Ph.D. from the University of Illinois at Chicago. He was a Doob Research Assistant Professor at the University of Illinois at Urbana-Champaign for three years. He then moved to California and is now teaching at California State University, Dominguez Hills. His research interests are in m...
متن کاملSUBSET SUMS IN Zp
Let Zp be the finite field of prime order p and A be a subset of Zp. We prove several sharp results about the following two basic questions: (1) When can one represent zero as a sum of distinct elements of A ? (2) When can one represent every element of Zp as a sum of distinct elements of A ?
متن کاملThe Inverse Problem on Subset Sums, II
For a set T of integers, let P (T ) be the set of all finite subset sums of T , and let T (x) be the set of all integers of T not exceeding x. Let B = {b1 < b2 < · · · } be a sequence of integers and d1 = 10, d2 = 3b1 + 4, and dn = 3bn−1 + 2 (n ≥ 3). In this paper, we prove that (i) if bn > dn for all n ≥ 1, then there exists a sequence of positive integers A = {a1 < a2 < · · · } such that, for...
متن کاملAsymptotically tight bounds on subset sums
For a subset A of a finite abelian group G we define Σ(A) = {∑a∈B a : B ⊂ A}. In the case that Σ(A) has trivial stabiliser, one may deduce that the size of Σ(A) is at least quadratic in |A|; the bound |Σ(A)| ≥ |A|2/64 has recently been obtained by De Vos, Goddyn, Mohar and Šámal [2]. We improve this bound to the asymptotically best possible result |Σ(A)| ≥ (1/4− o(1))|A|2. We also study a relat...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1998
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(98)80006-x