MathDB

Let

A

be a given set with

n

elements. Let

k<n

be a given positive integer. Find the maximum value of

m

for which it is possible to choose sets

B_i

and

C_i

for

i=1,2,\ldots,m

satisfying the following conditions:
[*]

B_i\subset A,

|B_i|=k,

[*]

C_i\subset B_i

(there is no additional condition for the number of elements in

C_i

), and [*]

B_i\cap C_j\neq B_j\cap C_i

for all

i\neq j.

Problem Statement