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

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* James Propp <jpropp@cs.uml.edu> [Jul 24. 2009 12:55]:

[...] 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?)

minp (MIN or Previous) maxn (MAX or Next) Not so fun to say but sufficiently suggestive. Symmetry suggests to call them omin and omax (where the 'o' is for 'outer', the direction of 'outer' is fixed by min and max already). Hmm...., mino and maxo ? These would look nicer: max_{+} and min_{-} ... and allow for max_{-} and min_{+} if ever needed. Symbols \vee and \wedge with subscripts + and - as needed?

Jim Propp