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AN IMPROVEMENT OF THE CONDITION FOR A SET OF POSITIVE INTEGERS TO BE SUBSET-SUM-DISTINCT.

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Title: AN IMPROVEMENT OF THE CONDITION FOR A SET OF POSITIVE INTEGERS TO BE SUBSET-SUM-DISTINCT.
Authors: Kamiyama, Yasulliko1 kamiyama@cs.u-ryukyu.ac.jp
Source: Advances & Applications in Discrete Mathematics. Nov2025, Vol. 42 Issue 8, p787-798. 12p.
Subjects: Integers, Number theory, Combinatorial optimization, Mathematics, Mathematical optimization, Combinatorics
Abstract: Let S be a set of positive integers. Then we say that S is a subset-sumdistinct set (briefly, S is an SSD-set) if for any two finite subsets X, Y of S, -X = Y. For fixed positive integers n and p, we set S, (n,p) : ={1p, 2p, 3p, ..., n} In our previous paper, we proved that S(,n, p) is an SSD-set when p > n. In this paper, we improve the bound as p > 0.71n. [ABSTRACT FROM AUTHOR]
Copyright of Advances & Applications in Discrete Mathematics is the property of Pushpa Publishing House and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
An: 191282013
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PubType: Academic Journal
PubTypeId: academicJournal
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  Data: AN IMPROVEMENT OF THE CONDITION FOR A SET OF POSITIVE INTEGERS TO BE SUBSET-SUM-DISTINCT.
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  Data: <searchLink fieldCode="AR" term="%22Kamiyama%2C+Yasulliko%22">Kamiyama, Yasulliko</searchLink><relatesTo>1</relatesTo><i> kamiyama@cs.u-ryukyu.ac.jp</i>
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  Data: <searchLink fieldCode="JN" term="%22Advances+%26+Applications+in+Discrete+Mathematics%22">Advances & Applications in Discrete Mathematics</searchLink>. Nov2025, Vol. 42 Issue 8, p787-798. 12p.
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  Data: <searchLink fieldCode="DE" term="%22Integers%22">Integers</searchLink><br /><searchLink fieldCode="DE" term="%22Number+theory%22">Number theory</searchLink><br /><searchLink fieldCode="DE" term="%22Combinatorial+optimization%22">Combinatorial optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics%22">Mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+optimization%22">Mathematical optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Combinatorics%22">Combinatorics</searchLink>
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  Data: Let S be a set of positive integers. Then we say that S is a subset-sumdistinct set (briefly, S is an SSD-set) if for any two finite subsets X, Y of S, -X = Y. For fixed positive integers n and p, we set S, (n,p) : ={1p, 2p, 3p, ..., n} In our previous paper, we proved that S(,n, p) is an SSD-set when p > n. In this paper, we improve the bound as p > 0.71n. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Advances & Applications in Discrete Mathematics is the property of Pushpa Publishing House and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.17654/0974165825050
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        Text: English
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        PageCount: 12
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    Subjects:
      – SubjectFull: Integers
        Type: general
      – SubjectFull: Number theory
        Type: general
      – SubjectFull: Combinatorial optimization
        Type: general
      – SubjectFull: Mathematics
        Type: general
      – SubjectFull: Mathematical optimization
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      – SubjectFull: Combinatorics
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      – TitleFull: AN IMPROVEMENT OF THE CONDITION FOR A SET OF POSITIVE INTEGERS TO BE SUBSET-SUM-DISTINCT.
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              M: 11
              Text: Nov2025
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