2018-11-stringbeginners-haruhi-problem-superpermutation

6f84f75ab93ad599bcf89a78dc5da8dc?s=47 kgoto
November 02, 2018

 2018-11-stringbeginners-haruhi-problem-superpermutation

ハルヒ問題、最小超置換の紹介
stringbeginners: https://sites.google.com/view/stringbeginners/workshop/2018/2018-11-02-tokyo

6f84f75ab93ad599bcf89a78dc5da8dc?s=128

kgoto

November 02, 2018
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  1. 2.

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    t ca : y op n h / r u s e m op 441 - 8-/ / 4 / 585.- 25 - 51 21 2.54 4-0/ 
  2. 3.

    ] ) 2 2 , .1 ! n )= O

    K [ ] S [ ) ] [ ] ( [= 
  3. 4.
  4. 5.

    ( 1,21,2. 3 3 ! n ( ) S )

    S = ( ) S         
  5. 6.

    N n i k + pe kc B B j

    k gD k p kc B][i k n - 1 p B][i k p :  P N B : B B kc
  6. 7.

    , 1 n , 1 9 A 3 ! "#$

    % "! ∑ "#$ % "! 6
  7. 8.

    1 , 1 n 9 T A ! "#$ %

    "! ∑ "#$ % "! 7 3 3
  8. 9.

    L n 4 2 1/ 8 0 28 A +

    8 8 )2 1 8 3 0 - ! ! ! ( A ,41 0 - ! ! ! (! ( ( L ) 8
  9. 10.

    A n , 3 9 80 +4 9 98 E

    n PT n PT n , 2 8 E n , 898 9 3 8 9 1 E 
  10. 11.

    = ∑ "#$ % "! ∑ "#$ % "!1 1

    n 1 ∑ "#$ $ "! = $1 
  11. 12.

    > ∑ "#$ % "! [ ]f >∑ "#$ %'$

    "! 4 [ . . 4 ! 4 [ e ( 4 [= ) e 2239 1239 S > e ( ( ( ( 4 , 4 [ [= e e 4 [ ! 4 , ( > , ( > ( ,  4 [ 4 - =
  12. 13.

    n - -,= = 2 c n 2 1 2,

    ] a 1 2,2 , [ = 2 , 2 1 - 2 2 3 4 2 2 2,2 , [ ,
  13. 14.

    = n ) = 0- S p 0- S >1

    0- S [ 4 2 0- = > 0- = [ 43  + = S ] S ] + = + = ( (
  14. 15.

    H L S n 0 ) 2 1 ] p

    2 1 e = ] 4 2 1 ] > 2 1 [ 2 1 [ > p 0 3 0 ( 2 1 = ] 0 -0 H L  0 ( -0 ] ] -0 0 ( -0 + 0 3 + 0 0 3 0
  15. 16.

    H n 3 - S p - = ! L

    p> ( ! ∑ "#$ %&$ "! + )! = ∑ "#$ % "!  3 2 ! ) ! 1 ) ! !
  16. 17.

    3 1 0 , n H ∑ "#$ % &!

    = 873 [ n 8 [ 2 ∑ ,#- . ,! ]5 [6 7 4 <5 6 5    ∑ ,#- . ,! 
  17. 18.

    , 2.113 n a [ ] c a n C

    .:0 .:0 2 8 === 4 2 : /. : 80 80 5 7 1
  18. 19.

    t 1 N S a / 1 (0 n l

    ms i E ] msN p N f o w p N oh u g r p !Nu N x rIC en l N rx p n l v Nu l N [ ) 2 2 1 2 . , . 2 2 8 1 : . 2 2 8 1 : 8  u u
  19. 20.

    . 4 S h[g]e 2. 4 3 n tr u

    o h iu S N p S l N w ps S wn m N p C!S S E C vN t rS x N n tr f S trS h ia  ,( ,) h[g]e pS I 8 4 1 /.0 . 1 4 = 1 4 = 8 :
  20. 21.

    g .,2 n ] [ .,2 n x 01 3

    - vt p01 3 - w u p- 01 3 - n e -0. ! -0. ! E e -0. ! -0. ! E a p u m rp u8 i ho r p p u m rp u8 i ho r p r p E 01 3 - 
  21. 22.

    +0 ] +0 ( n a 8 n ,1221 3

    [W ! ! ! i g E 
  22. 23.

    +8 8 (1408 - 2 P c n ,308 n

    i n 2534 r 2534 r h ] [ p m 1 1 51 1 0  le A)A oA (A 8 a s 0 5 8 E g l 8 8
  23. 24.

    -+ (02 , 1 ). P a] n 4 8[

    e P n c e - . e n = A = = = c e 
  24. 25.

    -+ : (02 , : 1 ). [ a P

    A [ a n 8 0 n 8 e c n 0 0 04 0 04 :: c n 4 8 0 04 0 04 :: ] e 4 8 
  25. 26.
  26. 27.

    n + + = n 0 + + ( (

    )( ( p( )( )( ( 1 ( p + - = c  a ,
  27. 28.

    n 1 - p 1( )++, p( 2 1, 2

    = c n 1 - 3 p 2 c n 
  28. 29.

    L 3 - p3 1 p- 1 ! p 1

    (! L n + 1! 1 ! 1 1 ! 1 (! 1 )! 1 )  - -/.- -/, 1 1 1 ! i a 1 ! - -/.- -/, c = ( /223 1 1 ! 1 1 1 ! 1 (! ( /223 c =