URN 
etd0625109115205 
Author 
Weicheng Hung 
Author's Email Address 
No Public. 
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Department 
Applied Mathematics 
Year 
2008 
Semester 
2 
Degree 
Master 
Type of Document 

Language 
zhTW.Big5 Chinese 
Title 
Inclusionexclusion and pigeonhole principles 
Date of Defense 
20090605 
Page Count 
116 
Keyword 
pigeonhole principle
Ramsey theorem
derangement
inclusionexclusion principle
consecutive permutation
Eulerâ€™s phi function
complete graph
combinations with repetition
onto function
rook polynomial
nonnegative integer solutions

Abstract 
In this paper, we will review two fundamental counting methods: inclusionexclusion and pigeonhole principles. The inclusionexclusion principle considers the elements of the sets satisfied some conditions, and avoids repeat counting by disjoint sets. We also use the inclusionexclusion principle to solve the problems of Euler phi function and the number of onto functions in number theory, and derangement and the number of nonnegative integer solutions of equations in combinatorics. We derive the closedform formula to those problems. For the forbidden positions problems, we use the rook polynomials to simplify the counting process. We also show the form of the inclusionexclusion principle in probability, and use it to solve some probability problems. The pigeonhole principle is an easy concept. We can establish some sets and use the pigeonhole principle to discuss the extreme value about the number of elements. Choose the pigeons and pigeonholes, properly, and solve problems by the concept of the pigeonhole principle. We also introduce the Ramsey theorem which is an important application of the pigeonhole principle. This theorem provides a method to solve problems by complete graph. Finally, we give some contest problems about the inclusionexclusion and pigeonhole principles to show how those principles are used. 
Advisory Committee 
MongNa Lo Huang  chair
MeiHui Guo  cochair
FuChuen Chang  advisor

Files 
indicate not accessible 
Date of Submission 
20090625 