OFFSET
1,3
COMMENTS
The representation of the partitions (for fixed n) is as (weakly) decreasing lists of parts, the order between individual partitions (for the same n) is co-lexicographic, see example. - Joerg Arndt, Sep 13 2013
LINKS
FORMULA
EXAMPLE
For n = 5 the partitions of 5 in colexicographic order are:
1+1+1+1+1
2+1+1+1
3+1+1
2+2+1
4+1
3+2
5
so the fifth row is the largest in each partition: 1,2,3,2,4,3,5
Triangle begins:
1;
1,2;
1,2,3;
1,2,3,2,4;
1,2,3,2,4,3,5;
1,2,3,2,4,3,5,2,4,3,6;
1,2,3,2,4,3,5,2,4,3,6,3,5,4,7;
1,2,3,2,4,3,5,2,4,3,6,3,5,4,7,2,4,3,6,5,4,8;
...
MATHEMATICA
colex[f_, c_]:=OrderedQ[PadRight[{Reverse[f], Reverse[c]}]];
Max/@Join@@Table[Sort[IntegerPartitions[n], colex], {n, 8}] (* Gus Wiseman, May 31 2020 *)
CROSSREFS
The sum of row n is A006128(n).
Row lengths are A000041.
Let y be the n-th integer partition in colexicographic order (A211992):
- The maximum of y is a(n).
- The length of y is A193173(n).
- The minimum of y is A196931(n).
- The Heinz number of y is A334437(n).
Lexicographically ordered reversed partitions are A026791.
Reverse-colexicographically ordered partitions are A026792.
Reversed partitions in Abramowitz-Stegun order (sum/length/lex) are A036036.
Reverse-lexicographically ordered partitions are A080577.
Lexicographically ordered partitions are A193073.
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Dec 10 2011
EXTENSIONS
Definition corrected by Omar E. Pol, Sep 12 2013
STATUS
approved