A334441 - OEIS

%I #17 Sep 22 2023 08:45:02

%S 0,1,2,1,3,2,1,4,2,3,2,1,5,3,4,2,3,2,1,6,3,4,5,2,3,4,2,3,2,1,7,4,5,6,

%T 3,3,4,5,2,3,4,2,3,2,1,8,4,5,6,7,3,4,4,5,6,2,3,3,4,5,2,3,4,2,3,2,1,9,

%U 5,6,7,8,3,4,4,5,5,6,7,3,3,4,4,5,6,2,3,3

%N Maximum part of the n-th integer partition in Abramowitz-Stegun (sum/length/lex) order; a(0) = 0.

%C First differs from A049085 at a(8) = 2, A049085(8) = 3.

%C The parts of a partition are read in the usual (weakly decreasing) order. The version for reversed (weakly increasing) partitions is A049085.

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

%e Triangle begins:

%e   0

%e   1

%e   2 1

%e   3 2 1

%e   4 2 3 2 1

%e   5 3 4 2 3 2 1

%e   6 3 4 5 2 3 4 2 3 2 1

%e   7 4 5 6 3 3 4 5 2 3 4 2 3 2 1

%e   8 4 5 6 7 3 4 4 5 6 2 3 3 4 5 2 3 4 2 3 2 1

%t Table[If[n==0,{0},Max/@Sort[IntegerPartitions[n]]],{n,0,10}]

%Y Row lengths are A000041.

%Y The length of the same partition is A036043.

%Y Ignoring partition length (sum/lex) gives A036043 also.

%Y The version for reversed partitions is A049085.

%Y a(n) is the maximum element in row n of A334301.

%Y The number of distinct parts in the same partition is A334440.

%Y Lexicographically ordered reversed partitions are A026791.

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

%Y Partitions in increasing-length colex order (sum/length/colex) are A036037.

%Y Graded reverse-lexicographically ordered partitions are A080577.

%Y Partitions counted by sum and number of distinct parts are A116608.

%Y Graded lexicographically ordered partitions are A193073.

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

%Y Partitions in dual Abramowitz-Stegun (sum/length/revlex) order are A334439.

%Y Cf. A001221, A103921, A124734, A185974, A296774, A299755, A334302, A334433, A334434, A334435, A334438.

%K nonn,tabf

%O 0,3

%A _Gus Wiseman_, May 06 2020