Re: [理工] [離散] 99中山資工

[jameschou (DOG)]

※ 引述《annheilong (方格子)》之銘言：
: 3. Find the coefficient of x^72 in (x^6 + X^7 + X^8 + ...)^10

(x^6 + x^7 + x^8 + ...)^10

= x^60 * (1 + x + x^2 + ... )^10


所以相當於求 (1 + x + x^2 + ... )^10 中 x^12項係數

  (1 + x + x^2 + ... )^10

= (1/1-x)^10

= (1-x)^(-10)

  ∞   -10
= Σ  C   *(-x)^i
  i=0  i

                            -10    21
代入 i=12可得 x^12項係數為 C    = C
                            12     12


: 4. Let A be a set with |A| = n, and let R be a binary
:    relation on A that is reflexive and antisymmetric.
:    (a) What is the maximum value for |R|
:    (b) How many antisymmetric relations can have this size?


(a)

1+2+3+...+n = n(n+1)/2

                       所以最多 n(n+1)/2 個

(b)

    n(n-1)/2
   2

             (就是二的1+2+...+(n-1)次方種)




這題不確定對不對..
我英文不太好不是很確定題意= ="


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