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Template:Orderings comparison table
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Since the partitions are sets of positive integers, the sets have different cardinality. For the sake of comparing the orderings of partitions, it is convenient to have sets with same cardinality by adding parts of value 0.
Lex and Colex, Ref Lex and Ref Colex, Rev Lex and Rev Colex, Rev Ref Lex and Rev Ref Colex constitute four pairs of conjugate partitions (transpose partitions) (Cf. Ferrers diagram.)
| Lex | Ref Lex |
Rev Lex |
Rev Ref Lex |
Colex | Ref Colex |
Rev Colex |
Rev Ref Colex |
| 1, 1, 1, 1, 1, 1 | 1, 1, 1, 1, 1, 1 | 6, 0, 0, 0, 0, 0 | 0, 0, 0, 0, 0, 6 | 6, 0, 0, 0, 0, 0 | 0, 0, 0, 0, 0, 6 | 1, 1, 1, 1, 1, 1 | 1, 1, 1, 1, 1, 1 |
| 2, 1, 1, 1, 1, 0 | 0, 1, 1, 1, 1, 2 | 5, 1, 0, 0, 0, 0 | 0, 0, 0, 0, 1, 5 | 5, 1, 0, 0, 0, 0 | 0, 0, 0, 0, 1, 5 | 2, 1, 1, 1, 1, 0 | 0, 1, 1, 1, 1, 2 |
| 2, 2, 1, 1, 0, 0 | 0, 0, 1, 1, 2, 2 | 4, 2, 0, 0, 0, 0 | 0, 0, 0, 0, 2, 4 | 4, 2, 0, 0, 0, 0 | 0, 0, 0, 0, 2, 4 | 2, 2, 1, 1, 0, 0 | 0, 0, 1, 1, 2, 2 |
| 2, 2, 2, 0, 0, 0 | 0, 0, 0, 2, 2, 2 | 4, 1, 1, 0, 0, 0 | 0, 0, 0, 1, 1, 4 | 3, 3, 0, 0, 0, 0 | 0, 0, 0, 0, 3, 3 | 3, 1, 1, 1, 0, 0 | 0, 0, 1, 1, 1, 3 |
| 3, 1, 1, 1, 0, 0 | 0, 0, 1, 1, 1, 3 | 3, 3, 0, 0, 0, 0 | 0, 0, 0, 0, 3, 3 | 4, 1, 1, 0, 0, 0 | 0, 0, 0, 1, 1, 4 | 2, 2, 2, 0, 0, 0 | 0, 0, 0, 2, 2, 2 |
| 3, 2, 1, 0, 0, 0 | 0, 0, 0, 1, 2, 3 | 3, 2, 1, 0, 0, 0 | 0, 0, 0, 1, 2, 3 | 3, 2, 1, 0, 0, 0 | 0, 0, 0, 1, 2, 3 | 3, 2, 1, 0, 0, 0 | 0, 0, 0, 1, 2, 3 |
| 3, 3, 0, 0, 0, 0 | 0, 0, 0, 0, 3, 3 | 3, 1, 1, 1, 0, 0 | 0, 0, 1, 1, 1, 3 | 2, 2, 2, 0, 0, 0 | 0, 0, 0, 2, 2, 2 | 4, 1, 1, 0, 0, 0 | 0, 0, 0, 1, 1, 4 |
| 4, 1, 1, 0, 0, 0 | 0, 0, 0, 1, 1, 4 | 2, 2, 2, 0, 0, 0 | 0, 0, 0, 2, 2, 2 | 3, 1, 1, 1, 0, 0 | 0, 0, 1, 1, 1, 3 | 3, 3, 0, 0, 0, 0 | 0, 0, 0, 0, 3, 3 |
| 4, 2, 0, 0, 0, 0 | 0, 0, 0, 0, 2, 4 | 2, 2, 1, 1, 0, 0 | 0, 0, 1, 1, 2, 2 | 2, 2, 1, 1, 0, 0 | 0, 0, 1, 1, 2, 2 | 4, 2, 0, 0, 0, 0 | 0, 0, 0, 0, 2, 4 |
| 5, 1, 0, 0, 0, 0 | 0, 0, 0, 0, 1, 5 | 2, 1, 1, 1, 1, 0 | 0, 1, 1, 1, 1, 2 | 2, 1, 1, 1, 1, 0 | 0, 1, 1, 1, 1, 2 | 5, 1, 0, 0, 0, 0 | 0, 0, 0, 0, 1, 5 |
| 6, 0, 0, 0, 0, 0 | 0, 0, 0, 0, 0, 6 | 1, 1, 1, 1, 1, 1 | 1, 1, 1, 1, 1, 1 | 1, 1, 1, 1, 1, 1 | 1, 1, 1, 1, 1, 1 | 6, 0, 0, 0, 0, 0 | 0, 0, 0, 0, 0, 6 |
