MathDB

For a positive integer

n

, there is a school with

n

people. For a set

X

of students in this school, if any two students in

X

know each other, we call

X

well-formed. If the maximum number of students in a well-formed set is

k

, show that the maximum number of well-formed sets is not greater than

3^{(n+k)/3}

.
Here, an empty set and a set with one student is regarded as well-formed as well.

Problem Statement