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2012 A Minimum Problem for Finite Sets of Real Numbers with Nonnegative Sum
G. Chiaselotti, G. Marino, C. Nardi
J. Appl. Math. 2012(SI03): 1-15 (2012). DOI: 10.1155/2012/847958

Abstract

Let n and r be two integers such that 0 < r n ; we denote by γ ( n , r ) [ η ( n , r ) ] the minimum [maximum] number of the nonnegative partial sums of a sum 1 = 1 n a i 0 , where a 1 , , a n are n real numbers arbitrarily chosen in such a way that r of them are nonnegative and the remaining n - r are negative. We study the following two problems: ( P 1 ) which are the values of γ ( n , r ) and η ( n , r ) for each n and r , 0 < r n ? ( P 2 ) if q is an integer such that γ ( n , r ) q η ( n , r ) , can we find n real numbers a 1 , , a n , such that r of them are nonnegative and the remaining n - r are negative with 1 = 1 n a i 0 , such that the number of the nonnegative sums formed from these numbers is exactly q ?

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G. Chiaselotti. G. Marino. C. Nardi. "A Minimum Problem for Finite Sets of Real Numbers with Nonnegative Sum." J. Appl. Math. 2012 (SI03) 1 - 15, 2012. https://doi.org/10.1155/2012/847958

Information

Published: 2012
First available in Project Euclid: 3 January 2013

zbMATH: 1273.11045
MathSciNet: MR2923380
Digital Object Identifier: 10.1155/2012/847958

Rights: Copyright © 2012 Hindawi

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Vol.2012 • No. SI03 • 2012
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