For sets $A,B \in [n]^{(r)}$, the $r$th layer of the Power set, we define the Ordering

$A < B$ if $A\neq B$ and $\max{(A\: \triangle \: B)} \in B$,

analogously to the Lexicographic order.

This is equivalent to $A < B$ if

$\sum\limits_{i \in A} 2^i < \sum\limits_{i \in B} 2^i$

Thus it can be thought as a 'binary' order.

It can be seen as the oppositie of {lexicographic order with the opposite ordering of the letter/numbers}