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• Emailcychen07_at_nuk.edu.tw
• ????401
• ?? http//www.csie.nuk.edu.tw/cychen/

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• Introduction to Combinatorial Mathematics
• by C. L. Liu

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• ?????????????????????????????????????????????,????
  ??????????,????????????????????,

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• 1. Recurrence Relations (????)
• ????????,???,???,??????,???,???,?????,???????
• 2. Permutation and Combinations (?????)
• ??,??,??????,??????,Stirling??
• 3. The Principle of Inclusion and Exclusion
  (????)
• ????,????
• 4. PÓ lyas Theory of Counting (PÓ lya????)
• ???????,Burnside??,??????,PÓ lya????

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• 1. Recurrence Relations (????)

Q merge sort Procedure sort(i, j) If
i j then return Xi else
begin m (i j -1)/2
return merge(sort(i m), sort(m 1,
j)) end T(n) the
computation time recurrence relation
T(n) T(n/2) T(n/2) (n -1) ? T(n)
2T(n/2) (n -1) if n ? 2 T(1)
0 A T(n) (log2n -1)n - 1
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• 2. Permutation and Combinations (?????)

Q ??????????,????????5?,????????5?????????? A 21
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5 0 0
4 1 0
4 0 1
3 2 0
3 1 1
3 0 2
2 3 0
2 2 1
2 1 2
2 0 3
1 4 0
1 3 1
1 2 2
1 1 3
1 0 4
0 5 0
0 4 1
0 3 2
0 2 3
0 1 4
0 0 5
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• 3. The Principle of Inclusion and Exclusion
  (????)

Q ??1?250??,??2, 3, 5, 7?????? A 57
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• 4. PÓ lyas Theory of Counting (PÓ lya????)

Q. ????????a, b, c, d, abc? d,???????,????x,
y??,???????? A 8
d abc y 3x y 2x1y y 1x2y y 3y
d abc x 3x x 2x1y x 1x2y x 3y
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• 1 ? Introduction
• 2 ? Recurrence Relations (????)-????????,???,???,
  
• 3 ? Recurrence Relations (????)-??????1
• 4 ? Recurrence Relations (????)-??????2 5
• 5 ? Recurrence Relations (????)-???,???
• 6 ? Recurrence Relations (????)-??????
• 7 ? Permutation and Combinations (?????)-??,??
• 8 ? Permutation and Combinations
  (?????)-??????,??????,Stirling??
• 9 ? ???
• 10 ? Generating function (????)
• 11 ? Generating function (????)-Ferrers graph
• 12 ? The Principle of Inclusion and Exclusion
  (????)
• 13 ? The Principle of Inclusion and Exclusion
  (????)-????
• 14 ? PÓlyas Theory of Counting
  (PÓlya????)-???????,
• 15 ? PÓlyas Theory of Counting
  (PÓlya????)-Burnside??,??????
• 16 ? PÓlyas Theory of Counting
  (PÓlya????)-PÓlya????
• 17-18? ???(??)

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• ??? 35
• ??? 40 (????5)
• ??(???,??) 25

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