kaleidoscopes, p295

の大域・局所問題を計算する．

{3,3,4}(1,0,0,0)・・・(8,24,32,16),(1,6,12,8)

{3,3,4}(0,1,0,0)・・・(24,96,96,24),(1,8,12,6)

{3,3,4}(0,0,1,0)・・・(32,96,88,24),(1,6,9,5)

{3,3,4}(0.0.0,1)・・・(16,32,24,8),(1,4,6,4)

{3,3,4}(1,1,0,0)・・・(48,120,96,24),(1,5,8,5)

{3,3,4}(1,0,1,0)・・・(96,288,240,48),(1,6,9,5)

{3,3,4}(1,0,0,1)・・・(64,192,208,80),(1,6,12,8)

{3,3,4}(0,1,1,0)・・・(96,192,120,24),(1,4,6,4)

{3,3,4}(0,1,0,1)・・・(96,288,248,56),(1,6,9,5)

{3,3,4}(0,0,1,1)・・・(64,128,88,24),(1,4,6,4)

{3,3,4}(1,1,1,0)・・・(192,384,240,48),(1,4,6,4)

{3,3,4}(1,1,0,1)・・・(192,480,368,80),(1,5,8,5)

{3,3,4}(1,0,1,1)・・・(192,480,368,80),(1,5,8,5)

{3,3,4}(0,1,1,1)・・・(192,384,248,56),(1,4,6,4)

{3,3,4}(1,1,1,1)・・・(384,768,464,80),(1,4,6,4)

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{3,3,4}(0,1,0,0)・・・(24,96,96,24),(1,8,12,6)これはbothなので問題なし

6 1　　

12 0　　

8 0 1

1 0 0 1

0 0 0 0 1

これにD4(8,-24,32,16,1)をかければOK

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1 1

4 0　　

4 0 1

1 0 0 1

0 0 0 0 1

これに(2,-1,3,3,1)をかけてもNG

これに(2,-1,4,4,1)をかければOK

最後の二重節点の位置は｛３，３｝（０１０）である．

｛３，３｝（０１０）の局所幾何（１，４，４，１）より

ｍ＝（２，-１，４，４，１）としてみる．

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1 1 1 1　

4 2 1 0　　

4 1 0 0

1 0 0 0

0 0 0 0 1

3方向から枝刈りすると仮定して

これに(4,-6,6,-1,1)をかければNG

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置換則は

(1)→(1)

(11)→(11)

(1,0,1)→(1,2,1)

(1,0,0,1)→(1,3,3,1)

(1,0,0,0,1)→(1,4,6,4,1)

(1,0,0,0,0,1)→(1,5,10,10,5,1) m+1Ck+1

であるが、最後の1はおまけなので・・・

(1,*,*,*,*,*)→ (1,*,*,*,*,*)

(0,1,*,*,*,*)→(2,1,*,*,*,*)

(0,0,1,*,*,*)→(3,3,1,*,*,*)

(0,0,0,1,*,*)→(4,6,4,1,*,*)

(0,0,0,0,1,*)→(5,10,10,5,1,*)

(0,0,0,0,0,1)→(6,15,20,15,6,1) m+1Ck+1

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[1]αn:

(*,*,*,*,*,1)→ (*,*,*,*,*,1)

(*,*,*,*,1,0)→(*,*,*,*,1,2)

(*,*,*,1,0,0)→(*,*,*,1,3,3)

(*,*,1,0,0,0)→(*,*,1,4,6,4)

(*,1,0,0,0,0)→(*,1,5,10,10,5)

(1,0,0,0,0,0)→(1,6,15,20,15,6) m+1Ck+1

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[1]βn:

(*,*,*,*,*,1)→ (*,*,*,*,*,1)

(*,*,*,*,1,0)→(*,*,*,*,1,2)

(*,*,*,1,0,0)→(*,*,*,1,4,4)これが適用される

(*,*,1,0,0,0)→(*,*,1,6,12,8)

(*,1,0,0,0,0)→(*,1,8,24,32,16)

(1,0,0,0,0,0)→(1,10,40,80,80,32) mCk2m-k

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[1]γn:

(1,*,*,*,*,*)→ (1,*,*,*,*,*)

(0,1,*,*,*,*)→(2,1,*,*,*,*)

(0,0,1,*,*,*)→(4,4,1,*,*,*)

(0,0,0,1,*,*)→(8,12,6,1,*,*)

(0,0,0,0,1,*)→(16,32,24,8,1,*)

[1]γn:

(*,*,*,*,*,1)→ (*,*,*,*,*,1)

(*,*,*,*,1,0)→(*,*,*,*,1,2)

(*,*,*,1,0,0)→(*,*,*,1,3,3)

(*,*,1,0,0,0)→(*,*,1,4,6,4)

(*,1,0,0,0,0)→(*,1,5,10,10,5)

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{3,4,3}

(1)→(1)

(11)→(11)

(1,0,1)→(1,2,1)

(1,0,0,1)→(1,4,4,1)

(1,*,*,*)→(1,*,*,*)

(0,1,*,*)→(2,1,*,*)

(0,0,1,*)→(3,3,1,*)

(0,0,0,1)→(6,12,8,1)

(*,*,*,1)→(*,*,*,1)

(*,*,1,0)→(*,*,1,2)

(*,1,0,0)→(*,1,3,3)

(1,0,0,0)→(1,8,12,6)

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{3,3,5}

(1)→(1)

(11)→(11)

(1,0,1)→(1,2,1)

(1,0,0,1)→(1,3,3,1)

(1,*,*,*)→(1,*,*,*)

(0,1,*,*)→(2,1,*,*)

(0,0,1,*)→(3,3,1,*)

(0,0,0,1)→(4,6,4,1,1)

(*,*,*,1)→(*,*,*,1)

(*,*,1,0)→(*,*,1,2)

(*,1,0,0)→(*,1,5,5)

(1,0,0,0)→(1,12,30,20)

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