Is there a special name for the following kind of function?
Let $f$ be a real-valued function over a partially ordered set $P$ such that for every chain $p_1 \le p_2 \le ... \le p_n$, there exists $j \in \{ 1, ..., n\}$ such that
- $f(p_1) \ge f(p_2) \ge ... \ge f(p_j)$, and
- $f(p_j) \le f(p_{j+1}) ... \le f(p_n)$.
That is, the function is unimodular when restricted to any chain in $P$.
My simulation data seems to behave like the function described above, but I cannot seem to find the right term for it. (The tag for graph theory is included due to the connection between partially ordered sets and directed acyclic graphs.)