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Underflip = Lincoln Loop + 180 with the 180 in the same direction that you are doing the lincoln loop (Left Lincoln + Left 180) Easiest way to explain it is left 90 + left lincoln + left 90. It cannot be Lincoln to 180 though, it has to be divided equally, as explained above.
Overflip = Lincoln Loop + 180 with the Lincoln in the oppoiste direction from the spin. Left 90 + right lincoln + lef 90. The spin and flip have to be divided like this, so that you arent doing lincoln to 180 which looks like a rodeo.
PIste is a French word meaning "track" literally, like on a CD, in French you'd have "Piste 3" instead of "track 3".
For skiing it refers to what in the US you call "trails". Doesn't matter if it's groomed or not; any area that is marked for skiing is a piste. Areas that are left natural but still patrolled are called "itinerant pistes".
So skis are rated on their on-piste suitability as how well they perform on the groomed runs, off-piste is anything more natural.
And a flair is like an underflip in the pipe I believe, underflips are awesome because it's pretty much all I can do.