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I am interested if the following concept has a name, or what do you think that a good name would be?

Let $\{X_{i}: i=1,2,\ldots,n,n+1\}$ be a family of posets and $F:X_{1}\times X_{2}\times\cdots\times X_{n}\rightarrow X_{n+1}$ such that $F$ is either increasing or decreasing with respect to each of the arguments (independently).

What would be an appropriate name for this property?

There is the concept of mixed monotone mapping, i.e., when $F:X_{1}\times X_{2}\rightarrow X_{3}$ is increasing in the first variable and decreasing in the second one, but I don't think that this name would be good to designate the more general concept above. I thought of generalized mixed monotone as a last resort, but I want to know your opinion on this.

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Coordinatewise monotonic? –  Arthur Fischer Jul 29 '12 at 16:42
    
@ArthurFischer: Is this a standard name or is it your personal suggestion? –  digital-Ink Jul 29 '12 at 16:49
    
Just a personal suggestion; I've never come across the concept before, but it seems like a natural name. –  Arthur Fischer Jul 29 '12 at 16:51
    
@ArthurFischer: A search on Google gave some good results on "Coordinate-wise monotonic" (and the related), which may lead me to believe that this is already standard terminology; I will keep investigate. –  digital-Ink Jul 29 '12 at 20:29

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