My instructor wants references about the indexation over the hypercube, related question here, he does not believe that I was the first who used it -- [update] thanks to a comment, the name is Hasse Diagram for posets. I have seen similar indexation in set-theory related to power-sets like the below. So
what is the historical background about naming vertices in a hypercube?
Example with the 3th Hypercube and the power-set of {1,2,3}
Helper questions
Is there someone who worked with power-sets and the axiom of power-set or Zermelo–Fraenkel set theory that used similar notation?
Is this somehow related to traversing a hypercube and anti-chains in a poset?