This site is supported by donations to The OEIS Foundation.

Template:Orderings comparison table

From OeisWiki
Jump to: navigation, search

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.)


Orderings comparison table for partitions of 6
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