منابع مشابه
A Note on the Postage Stamp Problem
Let h, k be fixed positive integers, and let A be any set of positive integers. Let hA := {a1 + a2 + · · · + ar : ai ∈ A, r ≤ h} denote the set of all integers representable as a sum of no more than h elements of A, and let n(h, A) denote the largest integer n such that {1, 2, . . . , n} ⊆ hA. Let n(h, k) = maxA n(h, A), where the maximum is taken over all sets A with k elements. The purpose of...
متن کاملGeneralizations of the Postage Stamp Problem
The postage stamp problem and its variations are classical problems in elementary number theory. This problem involves finding the largest value that cannot be expressed as a nonnegative linear combination of two relatively prime integers m and p. It turns out that this value can be defined as a function of m and p. An original proof of this fact is the first major goal of this paper. Moreover,...
متن کاملCompact Symmetric Solutions to the Postage Stamp Problem
We derive lower and upper bounds on possible growth rates of certain sets of positive integers Ak = {1 = a1 < a2 < . . . < ak} such that all integers n ∈ {0, 1, 2, . . . , kak} can be represented as a sum of no more than k elements of Ak, with repetition.
متن کاملThe Postage Stamp Problem and Essential Subsets in Integer Bases
Plagne recently determined the asymptotic behavior of the function E(h), which counts the maximum possible number of essential elements in an additive basis for N of order h. Here we extend his investigations by studying asymptotic behavior of the function E(h, k), which counts the maximum possible number of essential subsets of size k, in a basis of order h. For a fixed k and with h going to i...
متن کاملPostage stamp multiple anterior capsulorhexisotomies in pediatric cataract surgery
BACKGROUND Capsule related complications are common following pediatric cataract surgery. We report a new technique of multiple anterior capsulorhexisotomies after lens aspiration and intraocular lens (IOL) implantation. METHODS After performing automated lens aspiration, an IOL was implanted into the capsular bag. A bent 26 gauge needle was introduced through one side port and multiple small...
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ژورنال
عنوان ژورنال: British Journal of Psychiatry
سال: 1993
ISSN: 0007-1250,1472-1465
DOI: 10.1192/bjp.163.1.128a