1 Ocak 2010 Dergi makalesi Açık Erişim

Kolotoglu, Emre; Yazici, Emine Sule

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{
  "@context": "https://schema.org/", 
  "@id": 23967, 
  "@type": "ScholarlyArticle", 
  "creator": [
    {
      "@type": "Person", 
      "affiliation": "Koc Univ, Dept Math, TR-34450 Istanbul, Turkey", 
      "name": "Kolotoglu, Emre"
    }, 
    {
      "@type": "Person", 
      "affiliation": "Koc Univ, Dept Math, TR-34450 Istanbul, Turkey", 
      "name": "Yazici, Emine Sule"
    }
  ], 
  "datePublished": "2010-01-01", 
  "description": "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 >= 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 -> 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.", 
  "headline": "On Minimal Defining Sets of Full Designs and Self-Complementary Designs, and a New Algorithm for Finding Defining Sets of t-Designs", 
  "identifier": 23967, 
  "image": "https://aperta.ulakbim.gov.tr/static/img/logo/aperta_logo_with_icon.svg", 
  "license": "http://www.opendefinition.org/licenses/cc-by", 
  "name": "On Minimal Defining Sets of Full Designs and Self-Complementary Designs, and a New Algorithm for Finding Defining Sets of t-Designs", 
  "url": "https://aperta.ulakbim.gov.tr/record/23967"
}