I have to assume this is fairly common, but I'd like to know if there is a term for this technique, and what branch of mathematics it is a part of. (For reference, I have no formal training, but fell into a set of problems I need to solve, and I'm trying to understand the landscape.)
Forgive me if I'm expressing this poorly, and feel free to correct my notation and terminology:
For a set of numbers $1,2,3,4,$ where $0<n<5$
$4 + n = n$
$1 - n = 5 - n$
I understand this is analogous to a 2-bit register, and there's a problem involving reduction of symmetries in a 2^2 Latin square where this proved quite handy.