1 Ocak 2010 Dergi makalesi Açık Erişim

Kolotoglu, Emre; Yazici, Emine Sule

MARC21 XML

<?xml version='1.0' encoding='UTF-8'?>
<record xmlns="http://www.loc.gov/MARC21/slim">
  <leader>00000nam##2200000uu#4500</leader>
  <datafield tag="245" ind1=" " ind2=" ">
    <subfield code="a">On Minimal Defining Sets of Full Designs and Self-Complementary Designs, and a New Algorithm for Finding Defining Sets of t-Designs</subfield>
  </datafield>
  <datafield tag="909" ind1="C" ind2="4">
    <subfield code="p">GRAPHS AND COMBINATORICS</subfield>
    <subfield code="v">26</subfield>
    <subfield code="n">2</subfield>
    <subfield code="c">259-281</subfield>
  </datafield>
  <controlfield tag="001">23967</controlfield>
  <datafield tag="980" ind1=" " ind2=" ">
    <subfield code="a">user-tubitak-destekli-proje-yayinlari</subfield>
  </datafield>
  <datafield tag="520" ind1=" " ind2=" ">
    <subfield code="a">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.</subfield>
  </datafield>
  <datafield tag="650" ind1="1" ind2="7">
    <subfield code="2">opendefinition.org</subfield>
    <subfield code="a">cc-by</subfield>
  </datafield>
  <datafield tag="700" ind1=" " ind2=" ">
    <subfield code="u">Koc Univ, Dept Math, TR-34450 Istanbul, Turkey</subfield>
    <subfield code="a">Yazici, Emine Sule</subfield>
  </datafield>
  <datafield tag="980" ind1=" " ind2=" ">
    <subfield code="b">article</subfield>
    <subfield code="a">publication</subfield>
  </datafield>
  <datafield tag="542" ind1=" " ind2=" ">
    <subfield code="l">open</subfield>
  </datafield>
  <datafield tag="100" ind1=" " ind2=" ">
    <subfield code="u">Koc Univ, Dept Math, TR-34450 Istanbul, Turkey</subfield>
    <subfield code="a">Kolotoglu, Emre</subfield>
  </datafield>
  <datafield tag="260" ind1=" " ind2=" ">
    <subfield code="c">2010-01-01</subfield>
  </datafield>
  <controlfield tag="005">20210315112227.0</controlfield>
  <datafield tag="909" ind1="C" ind2="O">
    <subfield code="o">oai:zenodo.org:23967</subfield>
    <subfield code="p">user-tubitak-destekli-proje-yayinlari</subfield>
  </datafield>
  <datafield tag="856" ind1="4" ind2=" ">
    <subfield code="z">md5:30aaf304eeee3e803f7d1d33104405b3</subfield>
    <subfield code="s">209</subfield>
    <subfield code="u">https://aperta.ulakbim.gov.trrecord/23967/files/bib-43343f3e-2877-4621-96a1-93eda0b084ac.txt</subfield>
  </datafield>
  <datafield tag="540" ind1=" " ind2=" ">
    <subfield code="u">http://www.opendefinition.org/licenses/cc-by</subfield>
    <subfield code="a">Creative Commons Attribution</subfield>
  </datafield>
  <datafield tag="024" ind1=" " ind2=" ">
    <subfield code="a">10.1007/s00373-010-0892-2</subfield>
    <subfield code="2">doi</subfield>
  </datafield>
</record>