[考古] 組合數學/黃秀芬/96下期末考
※ [本文轉錄自 FCU_Talk 看板]
作者: coolsprite ( ) 看板: FCU_Talk
標題: [考題][資訊系][組合數學][黃秀芬 96下期末考]
時間: Sat Jun 21 20:10:58 2008
1.(15%) Find the number of permutations of a,b,c,...,x,y,z, in which none of
the patterns 'spin','game','path',or 'net' occurs.
1.(15%) Find the number of permutations of a, b, c, ... , x, y,z, in which
none of the patterns 'spin' , 'game' , 'path',or 'net' occurs
2.(15%) For the positive integers 1, 2, 3,..., n-1, n,there are 11660
derangements where 1, 2, 3, 4, 5, appear in the first five positions.
what is the value of n?
3.(10%) Determine the coefficient of x^3 in 1/[(x-2)(x-3)]?
4.(10%) Find the exponential generating function for the sequence
0!, 1!, 2!, 3! ....
5.(10%) A ship carries 48 flags, 12 each of the colors red, white, blue and
black.Twelve of these flag are placed on a vertical pole in order to
communicate a signal to other ship. How many of these signal use an
even number of blue and odd number of black flags?
6.(10%) Find a recurrence relation for the number of binary sequences of
length n that have no consecutive 1's.
7.(15%) Solve the recurrence relation a(n+2) - 6a(n+1) + 9a(n) = 3*2^n + 7*3^n
where n ≧ 0 and a(0) = 1 ,a(1) = 4.
***藍底白字括號部份代表下標字***
8.(15%) The following table make (R,+,．) into a ring, where R ={s,t,v,w,x,y}.
(1)What is the Zero for this ring?
(2)What is the addition inverse of x?
(3)Does R have a unity?
(4)Is R a integral domain?
(5)Is R a field?
┌─┬─────────┐ ┌─┬─────────┐
│＋│s t v w x y │ │．│s t v w x y │
├─┼─────────┤ ├─┼─────────┤
│ s│s t v w x y │ │ s│s s s s s s │
│ t│t v w x y s │ │ t│s t v w x y │
│ v│v w x y s t │ │ v│s v x s v x │
│ w│w x y s t v │ │ w│s w s w s w │
│ x│x y s t v w │ │ x│s x v s x v │
│ y│y s t v w x │ │ y│s y x w v t │
└─┴─────────┘ └─┴─────────┘
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