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I. Enumeration
A. Selections with and without repetitions (combinations &
permutations)
B. Partitions
1. Stirling numbers of the first and second kind
C. Principle of InclusionExclusion
1. Surjections
2. Derangements
3. Euler
±
function
D. Generating functions (ordinary and exponential)
1. For combinations and permutations
2. Solutions of recurrence relations
3. Catalan numbers
E. Pólya theory
II. Combinatorial designs
A. Design parameters
B. Balanced incomplete block designs (BIBDs)
C.
Partiallybalanced incomplete balanced designs (PBIBDs)
D. Triple systems
E. Resolvable designs
F. Finite geometries
1. Affine geometries
2. Projective geometries
3. Partial geometries
G. Latin squares
1.
Orthogonality
III. Matroids
A. Independence, basis, spanning, and cycle systems; rank function and closure
operator
1. The definition in terms of each of these
2. Proofs of equivalences of these definitions
B.
Duality
C. Representability
D. Greedy algorithm
IV. Pigeonhole principle and Ramsey's theorem
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 Spring '11
 NA
 Combinatorics, Permutations

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