Elementary Techniques for Erdos-Ko-Rado-like Theorems

Details Elementary Techniques for Erdos-Ko-Rado-like Theorems Elementary Techniques for Erdos-Ko-Rado-like Theorems

2008-08-06

arxiv.org/abs/0808.0774v2

Mathematics

Combinatorics

10 pages, 0 figures

Scientific paper

The well-known Erdos-Ko-Rado Theorem states that if F is a family of k-element subsets of {1,2,...,n} (n>2k-1) such that every pair of elements in F has a nonempty intersection, then |F| is at most $\binom{n-1}{k-1}$. The theorem also provides necessary and sufficient conditions for attaining the maximum. We present elementary methods for deriving generalizations of the Erdos-Ko-Rado Theorem on several classes of combinatorial objects. We also extend our results to systems under Hamming intersection.

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