Standard form for partitions of $Z_n$

Question

Let $A$ and $B$ be partitions of $Z_n$. Let's say that $A$ and $B$ are equivalent if $A=Bx+y$ for some $x\in{1,−1}$ and $y\in Z_n$. In other words, two partitions are equivalent if one can be obtained by inversion and/or transposition of the other. Suppose I wanted to make a list containing a single representative from each equivalence class. Is there a natural choice for equivalence class representative? I.e., is there a "standard form" for partitions of $Z_n$?