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 کاملRing-like DHTs and the Postage Stamp Problem
We explore Chord-like ring structures for Distributed Hash Tables (DHTs) and show that the Postage Stamp Problem (PSP) is equivalent to finding optimal structures for such ring topologies. We first leverage known results for that problem to design structures for ring-like DHTs that use shortest-path routing. We then describe a variant of the PSP that corresponds to ring-like DHTs that use greed...
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ژورنال
عنوان ژورنال: The Computer Journal
سال: 1969
ISSN: 0010-4620,1460-2067
DOI: 10.1093/comjnl/12.4.377