How can I determine the size of the largest collection

Oakey1w

Oakey1w

Answered question

2022-06-19

How can I determine the size of the largest collection of k-element subsets of an n-element set such that each pair of subsets has at most m elements in common?

Answer & Explanation

klemmepk

klemmepk

Beginner2022-06-20Added 16 answers

Let L be a set of m integers and F be an L-intersecting k-uniform family of subsets of a set of n elements, where m k, then
| F | ( n m )
k-uniform family is a set of subsets, each subset being of size k.
An L-intersecting family is such that the intersection size of any two distinct sets in the family is in L.
For every k m 1 and n 2 k 2 there exists a л-uniform family F of size > ( n 2 k ) m on n points such that | A B | m 1 for any two distinct sets A , B F.

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