组合数学的笔记(1)

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  ClarenceAu (Stay Hungry Stay Foolish)

  2.2 Permutations of Sets Theorem 2.2.1 For n and r positive integers with r <= n, P(n, r)=n*(n-1)* ……*(n-r-1)=n!/(n-r)! Theorem 2.2.2 The number of circular r-permutations of a set of n elements is given by P(n,r)/r=n!/r(n-r)! In particular, the number of circular permutations of n elements is (n-1)! 2.3 Combinations (Subsets) of Sets Theorem 2.3.1 For 0 <= r <= n, ... (更多)

  2.2 Permutations of Sets

  Theorem 2.2.1

  For n and r positive integers with r <= n, P(n, r)=n*(n-1)* ……*(n-r-1)=n!/(n-r)!

  Theorem 2.2.2

  The number of circular r-permutations of a set of n elements is given by P(n,r)/r=n!/r(n-r)! In particular, the number of circular permutations of n elements is (n-1)!

  2.3 Combinations (Subsets) of Sets

  Theorem 2.3.1

  For 0 <= r <= n, P(n,r) = r!C(n,r) Hence C(n,r) = n!/r!(n-r)!

  Corollary 2.3.2

  For 0 <= r <= n, C(n,r)=C(n, n-r)

  Theorem 2.3.3 (Pascal's Formula)

  For all integers n and k with 1 <= k <= n, C(n,k) = C(n-1,k) + C(n-1,k-1)

  Theorem 2.3.4

  For n >= 0 C(n,0)+C(n,1)+C(n,2)+...+C(n,n)=2^n, and the common value equals the number of subsets of an n-element set.

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  2011-02-11 09:07:23   回应

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