Computer Aided Knot Theory on Linux
| Project/Area Number | 15540072 |
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | NARA WOMEN'S UNIVERSITY |
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Principal Investigator |
OCHIAI Mitsuyuki Nara Women's University, Faculty of Science, Professor, 理学部, 教授 (70016179)
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| 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)
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| Project Period (FY) |
2003 – 2005
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| Project Status |
Completed(Fiscal Year 2005)
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| 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)
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| Keywords | Linux / 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 |
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| 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/
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Report
(4results)
Research Products
(10results)
