# Definition:Antilexicographic Order/General Definition

## Definition

Let $S_1, S_2, \ldots, S_n$ all be ordered sets.

Then we define $T_n$ as the antilexicographic order on $S_1, S_2, \ldots, S_n$ as:

$\forall n \in \N_{>0}: T_n = \begin {cases} S_1 & : n = 1 \\ T_{n - 1} \otimes^a S_n & : n > 1 \end {cases}$