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2005 Fiscal Year Final Research Report Summary

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)
Project Period (FY) 2003 – 2005
KeywordsLinux / knot / tangle / base tangle / polynomial invariant / mutant / Hecke algebras
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/

  • Research Products

    (6 results)

All 2005 2004 2003

All Journal Article (5 results) Book (1 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

    • Description
      「研究成果報告書概要(和文)」より
  • [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
  • [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
  • [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

    • Description
      「研究成果報告書概要(和文)」より
  • [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
  • [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

URL: 

Published: 2007-12-13  

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