The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A228531

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A228531

Triangle read by rows in which row n lists the partitions of n in reverse lexicographic order.
(history; published version)

#37 by Alois P. Heinz at Fri Sep 22 07:54:45 EDT 2023

STATUS

reviewed

approved

#36 by Joerg Arndt at Fri Sep 22 05:54:11 EDT 2023

STATUS

proposed

reviewed

#35 by Michel Marcus at Fri Sep 22 05:41:06 EDT 2023

STATUS

editing

proposed

#34 by Michel Marcus at Fri Sep 22 05:41:02 EDT 2023

LINKS

Wikiversity, <a href="https://en.wikiversity.org/wiki/Lexicographic_and_colexicographic_order"> Lexicographic and colexicographic order</a>

STATUS

approved

editing

#33 by Susanna Cuyler at Mon May 25 09:26:27 EDT 2020

STATUS

proposed

approved

#32 by Gus Wiseman at Mon May 25 03:22:10 EDT 2020

STATUS

editing

proposed

#31 by Gus Wiseman at Mon May 25 03:21:41 EDT 2020

CROSSREFS

Compositions under the same order (sum/revlex) are A066099 (triangle).

Reversed partitions in Abramowitz-Stegun order (sum/length/lex) are A036036.

Partitions in opposite Abramowitz-Stegun order (sum/length/revlex) are A334439.

Cf. A026792, A036036, A049085, A103921, A112798, A115623, A129129, A228351, A331581, A334435, A334439, A334442.

#30 by Gus Wiseman at Mon May 25 03:15:36 EDT 2020

COMMENTS

The name is correct if the partitions are read in reverse, so that the parts are weakly increasing. The version for non-reversed partitions is A080577. - Gus Wiseman, May 23 2020

#29 by Gus Wiseman at Sat May 23 01:33:49 EDT 2020

COMMENTS

The name is correct if the partitions are read in reverse, so that the parts are weakly increasing. The version for non-reversed partitions is A080577. - Gus Wiseman, May 23 2020

LINKS

OEIS Wiki, <a href="http://oeis.org/wiki/Orderings of partitions">Orderings of partitions</a>

Wikiversity, <a href="https://en.wikiversity.org/wiki/Lexicographic_and_colexicographic_order"> Lexicographic and colexicographic order</a>

MATHEMATICA

revlexsort[f_, c_]:=OrderedQ[PadRight[{c, f}]];

Join@@Table[Sort[Reverse/@IntegerPartitions[n], revlexsort], {n, 0, 8}] (* Gus Wiseman, May 23 2020 *)

CROSSREFS

Row lengths are A000041.

Partition sums are A036042.

Partition minima are A182715.

Partition lengths are A333486.

The lexicographic version (sum/lex) is A026791.

Compositions under the same order (sum/revlex) are A066099 (triangle).

The colexicographic version (sum/colex) is A080576.

The version for non-reversed partitions is A080577.

The length-sensitive version (sum/length/revlex) is A334302.

The Heinz numbers of these partitions are A334436.

Reversed partitions in Abramowitz-Stegun order (sum/length/lex) are A036036.

Partitions in colexicographic order (sum/colex) are A211992.

Partitions in lexicographic order (sum/lex) are A193073.

Partitions in opposite Abramowitz-Stegun order (sum/length/revlex) are A334439.

Cf. A000041, A066099, A026791, A026792, A211992, A049085, A103921, A112798, A115623, A129129, A228351, A331581, A334435, A334442.

STATUS

approved

editing

#28 by Joerg Arndt at Sat Sep 14 12:46:31 EDT 2013

STATUS

proposed

approved