I don't have any suggestions, but the operation vaguely reminds me of the logic of electron orbitals, where a new electron drops into the lowest orbital that doesn't already have two electrons. On Thu, Jul 23, 2009 at 8:07 PM, James Propp <jpropp@cs.uml.edu> wrote:
Has anyone encountered the operation
{ min(x,y) if x neq y, f(x,y) = { { x+1 if x = y
before, or the three related operations in which min is replaced by max and/or +1 is replaced by -1?
These operations have come up in my work, and I need symbols (and possibly names) for a couple of them; I'm guessing I'm not the first person to stumble upon them. E.g., note that if x, y, and z are the highest powers of 2 dividing integers a, b, and c that sum to zero, then z = f(x,y). But the two I need names and symbols for are actually { min(x,y) if x neq y, x-1 if x = y } and { max(x,y) if x neq y, x+1 if x = y }. (In my writeup-in-progress I've been calling them "smin" and "smax", but I no longer recall why I chose "s"; for "special", maybe?)
Jim Propp
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun