1 Ocak 2010 Dergi makalesi Açık Erişim

Kolotoglu, Emre; Yazici, Emine Sule

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  <identifier identifierType="URL">https://aperta.ulakbim.gov.tr/record/23967</identifier>
  <creators>
    <creator>
      <creatorName>Kolotoglu, Emre</creatorName>
      <givenName>Emre</givenName>
      <familyName>Kolotoglu</familyName>
      <affiliation>Koc Univ, Dept Math, TR-34450 Istanbul, Turkey</affiliation>
    </creator>
    <creator>
      <creatorName>Yazici, Emine Sule</creatorName>
      <givenName>Emine Sule</givenName>
      <familyName>Yazici</familyName>
      <affiliation>Koc Univ, Dept Math, TR-34450 Istanbul, Turkey</affiliation>
    </creator>
  </creators>
  <titles>
    <title>On Minimal Defining Sets Of Full Designs And Self-Complementary Designs, And A New Algorithm For Finding Defining Sets Of T-Designs</title>
  </titles>
  <publisher>Aperta</publisher>
  <publicationYear>2010</publicationYear>
  <dates>
    <date dateType="Issued">2010-01-01</date>
  </dates>
  <resourceType resourceTypeGeneral="Text">Journal article</resourceType>
  <alternateIdentifiers>
    <alternateIdentifier alternateIdentifierType="url">https://aperta.ulakbim.gov.tr/record/23967</alternateIdentifier>
  </alternateIdentifiers>
  <relatedIdentifiers>
    <relatedIdentifier relatedIdentifierType="DOI" relationType="IsIdenticalTo">10.1007/s00373-010-0892-2</relatedIdentifier>
  </relatedIdentifiers>
  <rightsList>
    <rights rightsURI="http://www.opendefinition.org/licenses/cc-by">Creative Commons Attribution</rights>
    <rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights>
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  <descriptions>
    <description descriptionType="Abstract">A defining set of a t-(v, k, lambda) design is a partial design which is contained in a unique t- design with the given parameters. A minimal defining set is a defining set, none of whose proper partial designs is a defining set. This paper proposes a new and more efficient algorithm that finds all non-isomorphic minimal defining sets of a given t- design. The complete list of minimal defining sets of 2-(6, 3, 6) designs, 2-(7, 3, 4) designs, the full 2-(7, 3, 5) design, a 2-(10, 4, 4) design, 2-(10, 5, 4) designs, 2-(13, 3, 1) designs, 2-(15, 3, 1) designs, the 2-(25, 5, 1) design, 3-(8, 4, 2) designs, the 3-(12, 6, 2) design, and 3-(16, 8, 3) designs are given to illustrate the efficiency of the algorithm. Also, corrections to the literature are made for the minimal defining sets of four 2-(7, 3, 3) designs, two 2-(6, 3, 4) designs and the 2-(21, 5, 1) design. Moreover, an infinite class of minimal defining sets for 2-((v)(3)) designs, where v &amp;gt;= 5, has been constructed which helped to show that the difference between the sizes of the largest and the smallest minimal defining sets of 2-((v)(3)) designs gets arbitrarily large as v -&amp;gt; infinity. Some results in the literature for the smallest defining sets of t-designs have been generalized to all minimal defining sets of these designs. We have also shown that all minimal defining sets of t-(2n, n, lambda) designs can be constructed from the minimal defining sets of their restrictions when t is odd and all t-(2n, n, lambda) designs are self-complementary. This theorem can be applied to 3-(8, 4, 3) designs, 3-(8, 4, 4) designs and the full 3-((8)(4)) design using the previous results on minimal defining sets of their restrictions. Furthermore we proved that when n is even all (n - 1)-(2n, n, lambda) designs are self-complementary.</description>
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