第65回情報科学談話会(村上 斉 教授)

Click here to load reader

Upload: gsis-gsis

Post on 16-Apr-2017

82 views

Category:

Science


0 download

TRANSCRIPT

fl

2016 6 30

()2016 6 30 1 / 16

()2016 6 30 2 / 16

()2016 6 30 2 / 16

()2016 6 30 2 / 16

()2016 6 30 2 / 16

15

2 2

()2016 6 30 2 / 16

2

()2016 6 30 3 / 16

2

2

()2016 6 30 3 / 16

2

2

()2016 6 30 3 / 16

2

2

()2016 6 30 3 / 16

2

2

()2016 6 30 3 / 16

2

2

()2016 6 30 3 / 16

2

2

()2016 6 30 3 / 16

2 2

1522

()2016 6 30 3 / 16

2 2

1522

[2] [2, 2]

()2016 6 30 3 / 16

()2016 6 30 4 / 16

8 3

()2016 6 30 4 / 16

8 3

()2016 6 30 4 / 16

8 3

[2, 1, 2]

()2016 6 30 4 / 16

8 3

[2, 1, 2]

3 8 2 +1

1 +

12

32

312= 2 += 2 +

()2016 6 30 4 / 16

8 3

[2, 1, 2]

8 2 +1

1 +31

2

32

312= 2 += 2 +

22 5 2 + 1

()2016 6 30 4 / 16

()2016 6 30 5 / 16

()2016 6 30 5 / 16

1

2 +2

()2016 6 30 5 / 16

1

2 +2

1 +

212 +1

()2016 6 30 5 / 16

1

()2016 6 30 6 / 16

1

()2016 6 30 6 / 16

1

()2016 6 30 6 / 16

2

()2016 6 30 7 / 16

2

()2016 6 30 7 / 16

2

()2016 6 30 7 / 16

2

()2016 6 30 7 / 16

2

()2016 6 30 7 / 16

2

()2016 6 30 7 / 16

2

()2016 6 30 7 / 16

2

()2016 6 30 7 / 16

1

()2016 6 30 8 / 16

1

()2016 6 30 8 / 16

1

52

()2016 6 30 8 / 16

1

512 2 + 2

()2016 6 30 8 / 16

1

512 2 + 2

()2016 6 30 8 / 16

1

512 2 + 2

()2016 6 30 8 / 16

1

512 2 + 2

()2016 6 30 8 / 16

1

512 2 + 2

=

()

2016 6 30 8 / 16

2

()2016 6 30 9 / 16

2

81

1 +

23 2 +1

()2016 6 30 9 / 16

2

81

1 +

23 2 +1

2

=

()2016 6 30 9 / 16

2

81

1 +

23 2 +1

2

=

()2016 6 30 9 / 16

()2016 6 30 10 / 16

()2016 6 30 10 / 16

275

()2016 6 30 10 / 16

275= 5 +

25

()2016 6 30 10 / 16

2725

1

= 5 += 5 +552

()2016 6 30 10 / 16

2725

2= 5 += 5 += 5 +5511

2 +

21

()2016 6 30 10 / 16

2272115

2 +

2= 5 += 5 += 5 +551

()2016 6 30 10 / 16

2272115

2 +

2= 5 += 5 += 5 +551

275

()2016 6 30 10 / 16

2272115

2 +

2= 5 += 5 += 5 +551

273= 6 +55

()2016 6 30 10 / 16

2272115

2 +

2= 5 += 5 += 5 +551

273= 6 += 6 +551

53

()2016 6 30 10 / 16

2272115

2 +

2= 5 += 5 += 5 +551

551

53 27 3= 6 += 6 += 6 +1

12 + 3

()2016 6 30 10 / 16

2272115

2 +

2= 5 += 5 += 5 +551

551

53 27 3= 6 += 6 += 6 +1

12 + 3

()2016 6 30 10 / 16

2272115

2 +

2= 5 += 5 += 5 +551

551

53 27 3= 6 += 6 += 6 +1

12 + 3

2

()2016 6 30 10 / 16

2272115

2 +

2= 5 += 5 += 5 +551

551

53 27 3= 6 += 6 += 6 +1

12 + 3

2 (Conway (1970))

()2016 6 30 10 / 16

()2016 6 30 11 / 16

()2016 6 30 11 / 16

171

2= 3 +52 + 1

()2016 6 30 11 / 16

171

2= 3 +52 + 1

171

3= 2 +72 + 1

()2016 6 30 11 / 16

171

2= 3 +52 + 1

171

3= 2 +72 + 1

()2016 6 30 11 / 16

171

2= 3 +52 + 1

171

3= 2 +72 + 1

(Schubert (1956))

lqppqlq q 1 (mod p)

()2016 6 30 11 / 16

171

2= 3 +52 + 1

171

3= 2 +72 + 1

(Schubert (1956))

lqppqlq q 1 (mod p) 5 7 17 = 2 1.

()2016 6 30 11 / 16

171

2= 3 +52 + 1

171

3= 2 +72 + 1

(Schubert (1956))

lqppqlq q 1 (mod p) 5 7 17 = 2 1.5717 = 17

()2016 6 30 11 / 16

()2016 6 30 12 / 16

()2016 6 30 12 / 16

271

2= 5 +52 + 1

()2016 6 30 12 / 16

271

2= 5 +52 + 1

()2016 6 30 12 / 16

271

2= 5 +52 + 1

()2016 6 30 12 / 16

271

2= 5 +52 + 1

=

3 +1

2 + 1217=

5

()2016 6 30 12 / 16

271

2= 5 +52 + 1

=

3 +1

2 + 1217=

5=

2 +1

2 + 1317=

7

()2016 6 30 12 / 16

()2016 6 30 13 / 16

3117

2 + 2 + 1 = 7

()2016 6 30 13 / 16

3117

2 + 2 + 1 = 7

()2016 6 30 13 / 16

3117

2 + 2 + 1 = 7

()2016 6 30 13 / 16

3117

2 + 2 + 1 = 7

=

3

()2016 6 30 13 / 16

3117

2 + 2 + 1 = 7

=

3

1

()2016 6 30 13 / 16

3117

2 + 2 + 1 = 7

=

3

1

=

()2016 6 30 13 / 16

3117

2 + 2 + 1 = 7

=

3

1

=

271717557= 3 1

()2016 6 30 13 / 16

()2016 6 30 14 / 16

()2016 6 30 14 / 16

3117

2 +=2 + 17

()2016 6 30 14 / 16

3117

2 +=2 + 17

=

5

()2016 6 30 14 / 16

3117

2 +=2 + 17

=

5

3

()2016 6 30 14 / 16

3117

2 +=2 + 17

=

5

3

1

()2016 6 30 14 / 16

3117

2 +=2 + 17

=

5

3

1

177'\i3 1

5

()2016 6 30 14 / 16

1

()2016 6 30 15 / 16

1

()2016 6 30 15 / 16

1

177'\i3 1

5

()2016 6 30 15 / 16

1

177'\i3 1

5

7 17 2

()2016 6 30 15 / 16

1

177'\i3 1

5

7 17 2 2

()2016 6 30 15 / 16

1

177'\i3 1

5

17 2 2

7

()2016 6 30 15 / 16

1

()2016 6 30 16 / 16

1

(KanenobuHM (1986))

p

2n2 n m 2mn = p 1 [a, a1, a2, . . . , ak , 2, ak , . . . , a2, a1]

()2016 6 30 16 / 16

1

(KanenobuHM (1986))

p

2n2 n m 2mn = p 1 [a, a1, a2, . . . , ak , 2, ak , . . . , a2, a1]

p = 19, m = 5, n = 2 19 = 2 +1

81

2 +1 + 12.

()2016 6 30 16 / 16

1

(KanenobuHM (1986))

p

2n2 n m 2mn = p 1 [a, a1, a2, . . . , ak , 2, ak , . . . , a2, a1]

p = 19, m = 5, n = 2 19 = 2 +1

81

2 +1 + 12. 19

= 3 +81

1

2 + 2 + 12

()2016 6 30 16 / 16