76.結び目理論におけるDowker,Thistlethwaiteのアルゴリズムに基づく1つのcomputer program

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We set up a computer programming to list up sequences corresponding to knot projections using Dowker-Thistlethwaite's algorism. Take a point P and a direction on a knot projection, traverse from P via the knot projection and label the crossing point in order. Since we across a crossing point twice, each crossing point has two labels. So if the knot projection has n crossing points, we get a sequence with 2n letters, i.e. a permutation (a_1, a_2...,a_<2n>) of 1, 2,...,2n, so that i and a_i are the labels corresponding to a same crossing point. So the mapping a: {1, 2,..., 2n}→{1, 2..., 2n} defined by a(i)=a_i satisfies a^2=id. and has a parity reversing. Dowker-Thistlethwaite gave necessary and sufficient conditions for a mapping a (or a permutation (a_1, a_2,..., a_<2n>)) corresponding to a knot projection. As their conditions are fitting into a computer programming, we set up a programming to list up sequences satisfying Dowker-Thistlethwaite conditions. We use N_<88>-BASIC as the programming language and a personal computer, PC9801 (NEC).
東京女子大学の論文
1988-03-15