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The equal–sum–free subset problem

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Abstract

Given a set W of positive integers, a set I ⊆ W is independent if all the partial sums in I are distinct. We prove estimates on the maximum size of an independent set within a set of n integers.

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Authors and Affiliations

  1. Institute for Computer Science and Control, 1111, Budapest, Kende u. 13, Hungary

    Gábor Bacsó

  2. Alfréd Rényi Institute of Mathematics, 1053, Budapest, Reáltanoda u. 13-15, Hungary

    Gábor Bacsó

  3. Department of Computer Science and Systems Technology, University of Pannonia, H-8200, Veszprém, Egyetem u. 10, Hungary

    Zsolt Tuza

Authors
  1. Gábor Bacsó
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  2. Zsolt Tuza
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Corresponding author

Correspondence to Gábor Bacsó.

Additional information

Supported by the ERC Consolidator Grant SYSTEMATICGRAPH (No. 725978) of the European Research Council.

Supported in part by the National Research, Development and Innovation Office–NKFIH under the grant SNN 129364, and by the Széchenyi 2020 grant EFOP-3.6.1–16–2016–00015.

Communicated by P. Hajnal

Acknowledgment.

We would like to thank the referee for his/her constructive comments, and in particular for inviting our attention to the balanced ternary numeral system concerning the proof of Theorem 2.1.

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Bacsó, G., Tuza, Z. The equal–sum–free subset problem. ActaSci.Math. 86, 73–79 (2020). https://doi.org/10.14232/actasm-019-871-5

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  • DOI: https://doi.org/10.14232/actasm-019-871-5

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