 Last-to-first mapping

In a sorted cyclic rotation matrix, the last-to-first mapping sends the $k$th occurrence of a character in the last column to its $k$th occurrence in the first column. For one-based rows, $\mathrm{LF}(r)=C(L_r)+\mathrm{Occ}(L_r,r)$, where $C(c)$ counts smaller characters and $\mathrm{Occ}(c,r)$ counts $c$ in the first $r$ entries of the last column. It moves a rotation's start one character backwards cyclically. Equal characters retain the lexicographic order of their following sequences, which proves the occurrence-order rule.^[ref]