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 Probl. Peredachi Inf., 2012, Volume 48, Issue 4, Pages 56–61 (Mi ppi2095)

Large Systems

A remark on the problem of nonnegative $k$-subset sums

H. Aydiniana, V. M. Blinovskyab

a Department of Mathematics, University of Bielefeld, Germany
b Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow

Abstract: Given a set of $n$ real numbers with a nonnegative sum, consider the family of all its $k$-element subsets with nonnegative sums. How small can the size of this family be? We show that this problem is closely related to a problem raised by Ahlswede and Khachatrian in [1]. The latter, in a special case, is nothing else but the problem of determining a minimal number $c_n(k)$ such that any $k$-uniform hypergraph on $n$ vertices having $c_n(k)+1$ edges has a perfect fractional matching. We show that results obtained in [1] can be applied for the former problem. Moreover, we conjecture that these problems have in general the same solution.

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English version:
Problems of Information Transmission, 2012, 48:4, 347–351

Bibliographic databases:

UDC: 621.391.1+519.1
Revised: 31.07.2012

Citation: H. Aydinian, V. M. Blinovsky, “A remark on the problem of nonnegative $k$-subset sums”, Probl. Peredachi Inf., 48:4 (2012), 56–61; Problems Inform. Transmission, 48:4 (2012), 347–351

Citation in format AMSBIB
\Bibitem{AidBli12} \by H.~Aydinian, V.~M.~Blinovsky \paper A remark on the problem of nonnegative $k$-subset sums \jour Probl. Peredachi Inf. \yr 2012 \vol 48 \issue 4 \pages 56--61 \mathnet{http://mi.mathnet.ru/ppi2095} \transl \jour Problems Inform. Transmission \yr 2012 \vol 48 \issue 4 \pages 347--351 \crossref{https://doi.org/10.1134/S0032946012040059} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000314036400005} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. M. Blinovsky, “Minimum number of edges in a hypergraph guaranteeing a perfect fractional matching and the MMS conjecture”, Problems Inform. Transmission, 50:4 (2014), 340–349
2. Chowdhury A., Sarkis G., Shahriari Sh., “the Manickam-Miklos-Singhi Conjectures For Sets and Vector Spaces”, J. Comb. Theory Ser. A, 128 (2014), 84–103
3. F. Ihringer, “A Note on the Manickam-Miklos-Singhi Conjecture For Vector Spaces”, Eur. J. Comb., 52:A (2016), 27–39
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