منابع مشابه
Integer Sets with Distinct Subset - Sums
In Section 1 we introduce the problem of finding minimal-height sets of n natural numbers with distinct subset-sums (SSD), and in Section 2 review the well-known Conway-Guy sequence u, conjectured to yield a minimal SSD set for every n. We go on (Section 3) to prove that u certainly cannot be improved upon by any "greedy" sequence, to verify numerically (Section 4) that it does yield SSD sets f...
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We study the problem of determining the minimal degree d(m) of a polynomial that has all coefficients in {0, 1} and a zero of multiplicity m at −1. We show that a greedy solution is optimal precisely when m ≤ 5, mirroring a result of Boyd on polynomials with ±1 coefficients. We then examine polynomials of the form ∏ e∈E(x e+ 1), where E is a set of m positive odd integers with distinct subset s...
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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).
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We say that a family {xi | i ∈ [m]} of vectors in a Banach space X satisfies the k-collapsing condition if ‖∑i∈I xi‖ ≤ 1 for all k-element subsets I ⊆ {1,2, . . . ,m}. Let C (k,d) denote the maximum cardinality of a k-collapsing family of unit vectors in a d-dimensional Banach space, where the maximum is taken over all spaces of dimension d. Similarly, let C B(k,d) denote the maximum cardinalit...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1988
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1988-0917837-5