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University of Victoria Notes for Math 322: Intermediate Combinatorics (version 5 April 2011)

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Author(s): Peter Dukes, Gary MacGillivray
Year: 2011

Language: English
Commentary: Downloaded from http://www.math.uvic.ca/faculty/jing/322notes.pdf

1 Generating Subsets and Permutations 1
2 Systems of Distinct Representatives 11
3 Posets and extremal set theory 19
4 Finite geometries 29
5 Latin squares 41
6 Designs 55
6.1 Basic results and existence . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
6.2 Fisher’s inequality and symmetric designs . . . . . . . . . . . . . . . . . . 62
6.3 Difference sets and difference systems . . . . . . . . . . . . . . . . . . . . . 68
6.4 Resolvable designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
6.5 Steiner triple systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
7 Codes 81
7.1 Basic properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
7.2 Linear codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
7.3 Hamming codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
Bibliography 101