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Math 239: Intro to combinatorics and optimization
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Math 239: Intro to combinatorics and optimization
Math 239: Intro to combinatorics and optimization
Lists
The list of a set S is a list of the elements of S exactly once each, in some order.
Example:
S = {dog, 2, z}
All of the lists that can be generated from S are
dog,2,z 2,dog,z z,dog,2
dog,z,2 2,z,dog z,2,dog
Permutation
A permutation is a list of the set {1, 2, ....., n} for some n belongs to N
Partial Lists
Injection
Surjection
Bijection
n Choose k
If there is a bijection between A and B, then mod(A) = mode(B)
Multiset
Permutations
Combinations
Theorem 1.9
Power Series
Binomial theorem
Generating series
Negative Binomials
Negative Binomial Theorem
Coefficient extraction
Generating series with respect to 'w’
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