2009.1.7 Poset time

While we're off in discrete-math land, I might as well continue with something that I've wondered about vaguely for quite a while but only really bothered to figure out a month or two ago, which is, what does the poset of all LCD/calculator-style numerals with respect to subset inclusion of their LCD cells look like? What does that opaquely-articulated question even mean? Well, this is what it looks like, and you can probably figure out just by looking at it what I mean:

What we see is that 8 includes each of the other numerals (which follows from the fact that every LCD cell is turned on in 8); 9, meanwhile, includes a surprisingly large number of numerals, namely five; and 1 is the only numeral that is "three degrees of inclusion" away from 8. The quasi-symmetrical configuration of rows by one-four-four-one is kind of cool. I looked into expanding this to LCD letters as well, but that became a tangled mess. Maybe I'll try to show as neat a version of it as possible at some point, though.