2005 Fiscal Year Final Research Report Summary
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)
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| Project Period (FY) |
2003 – 2005
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| Keywords | Linux / knot / tangle / base tangle / polynomial invariant / mutant / Hecke algebras |
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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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