MathDB

Let

m

and

n

be positive integers integers such that

2m + 1 < n

, and let

S

be the set of the

2^n

subsets of

\{1,2,\ldots,n\}

. Prove that we can place the elements of

S

on a circle, so that for any two adjacent elements

A

and

B

, the set

A \Delta B

has exactly

2m + 1

elements.
Note:

A \Delta B = (A \cup B) - (A \cap B)

is the set of elements that are exclusively in

A

or exclusively in

B

Problem Statement