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Computer Aided Knot Theory on Linux

Research Project

Project/Area Number 15540072
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionNARA WOMEN'S UNIVERSITY

Principal Investigator

OCHIAI Mitsuyuki  Nara Women's University, Faculty of Science, Professor, 理学部, 教授 (70016179)

Co-Investigator(Kenkyū-buntansha) KAKO Fujio  Nara Women's University, Faculty of Science, Professor, 理学部, 教授 (90152610)
鴨 浩靖  奈良女子大学, 理学部, 助手 (20243355)
新出 尚之  奈良女子大学, 理学部, 講師 (40208111)
Project Period (FY) 2003 – 2005
Project Status Completed (Fiscal Year 2005)
Budget Amount *help
¥3,100,000 (Direct Cost: ¥3,100,000)
Fiscal Year 2005: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2004: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2003: ¥1,200,000 (Direct Cost: ¥1,200,000)
KeywordsLinux / knot / tangle / base tangle / polynomial invariant / mutant / Hecke algebras / 3並行化HOMFLY多項式 / Hecke環 / ブレイド / 多項式不変量 / 不変量
Research Abstract

(1)We made Matrix representations of Hecke algebras H(q,n) of n up to 18.
(2)We made a computer program bTd to assist knot researchers about the followings :
(2.1) to compute base tangle decompositions of n-tangles with 1<n<10.
(2.2) to compute HOMELY polynomials of knots and links using tangle decompositions
(3)HEAD INVESTIGATOR writes a paper "Base Tangle Decompositions of n-string tangles with 1<n<10" submitted to Experimental Mathematics
(4)We had founded two mutant knots K1 and K2 with 12 crossings such that P(K1^3;x,y) equals to P(K2^3;x,y) but P(K1^4;x,y) does not equal to P(K2^4 ;x,y).
(5)Our software bTd had been opened at http://amadeus.ics.nara-wu.ac.jp/~ochiai/

Report

(4 results)
  • 2005 Annual Research Report   Final Research Report Summary
  • 2004 Annual Research Report
  • 2003 Annual Research Report
  • Research Products

    (10 results)

All 2005 2004 2003 Other

All Journal Article (6 results) Book (1 results) Publications (3 results)

  • [Journal Article] Lascoux-Schutzenbergerの算法によるHecke環の線形表現の構成2005

    • Author(s)
      加古 富志雄
    • Journal Title

      奈良女子大学人間文化研究科年報 20

      Pages: 321-333

    • NAID

      110008667543

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Computational Constructions of Representation Matrixes of Hecke algebras by Lascoux-Schutzenberger method (in Japanese)2005

    • Author(s)
      F.Kako
    • Journal Title

      ANNUAL REPORTS OF GRAUATE SCHOOL OF HUMANITIES AND SCIENCES

      Pages: 321-333

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Lascoux-Schutzenbergerの算法によるHeche環の線形表現の構成2005

    • Author(s)
      加古富志雄
    • Journal Title

      奈良女子大学研究年報 20

      Pages: 321-333

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Graph Theory with Applications to Planar Graphs (in Japanese)2004

    • Author(s)
      M.Ochiai
    • Journal Title

      Nihon-shouronnsha

      Pages: 1-186

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] 結び目とコンピュータ2003

    • Author(s)
      落合 豊行
    • Journal Title

      数学セミナー(日本評論社) 4号-12号(総)

      Pages: 54-54

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Knot Theory by Computer (in Japanese)2003

    • Author(s)
      M.Ochiai
    • Journal Title

      Nihon-shouronnsha

      Pages: 4-12

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Book] グラフ理論入門-平面グラフへの応用2004

    • Author(s)
      落合 豊行
    • Total Pages
      186
    • Publisher
      日本評論社
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Publications] 落合豊行: "結び目とコンピュータ"数学セミナー(日本評論社). 4-11. (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] 落合豊行, 坂田宜子: "結び目とコンピュータ"数学セミナー(日本評論社). 12. (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] 落合豊行: "グラフ理論入門-平面グラフへの応用"日本評論社. 1-186 (2004)

    • Related Report
      2003 Annual Research Report

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Published: 2003-04-01   Modified: 2016-04-21  

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