cp's OEIS Frontend

A344087 Flattened tetrangle of strict integer partitions sorted first by sum, then colexicographically.

%I A344087 #10 Sep 22 2023 09:02:38
%S A344087 1,2,2,1,3,3,1,4,4,1,3,2,5,3,2,1,5,1,4,2,6,4,2,1,6,1,5,2,4,3,7,5,2,1,
%T A344087 4,3,1,7,1,6,2,5,3,8,6,2,1,5,3,1,8,1,4,3,2,7,2,6,3,5,4,9,4,3,2,1,7,2,
%U A344087 1,6,3,1,5,4,1,9,1,5,3,2,8,2,7,3,6,4,10
%N A344087 Flattened tetrangle of strict integer partitions sorted first by sum, then colexicographically.
%C A344087 The zeroth row contains only the empty partition.
%C A344087 A tetrangle is a sequence of finite triangles.
%H A344087 Wikiversity, <a href="https://en.wikiversity.org/wiki/Lexicographic_and_colexicographic_order">Lexicographic and colexicographic order</a>
%e A344087 Tetrangle begins:
%e A344087   0: ()
%e A344087   1: (1)
%e A344087   2: (2)
%e A344087   3: (21)(3)
%e A344087   4: (31)(4)
%e A344087   5: (41)(32)(5)
%e A344087   6: (321)(51)(42)(6)
%e A344087   7: (421)(61)(52)(43)(7)
%e A344087   8: (521)(431)(71)(62)(53)(8)
%e A344087   9: (621)(531)(81)(432)(72)(63)(54)(9)
%t A344087 colex[f_,c_]:=OrderedQ[PadRight[{Reverse[f],Reverse[c]}]];
%t A344087 Table[Sort[Select[IntegerPartitions[n],UnsameQ@@#&],colex],{n,0,10}]
%Y A344087 Positions of first appearances are A015724.
%Y A344087 Triangle sums are A066189.
%Y A344087 Taking revlex instead of colex gives A118457.
%Y A344087 The not necessarily strict version is A211992.
%Y A344087 Taking lex instead of colex gives A344086.
%Y A344087 A026793 gives reversed strict partitions in A-S order (sum/length/lex).
%Y A344087 A319247 sorts strict partitions by Heinz number.
%Y A344087 A329631 sorts reversed strict partitions by Heinz number.
%Y A344087 A344090 gives strict partitions in A-S order (sum/length/lex).
%Y A344087 Cf. A005117, A014466, A209862.
%Y A344087 Partition/composition orderings: A026791, A026792, A036036, A036037, A048793, A066099, A080576, A080577, A112798, A124734, A162247, A193073, A211992, A228100, A228351, A228531, A246688, A272020, A299755, A296774, A304038, A319247, A334301, A334302, A334439, A334442, A335122, A339351, A344085, A344086, A344088, A344089, A344091.
%Y A344087 Partition/composition applications: A001793, A005183, A036043, A049085, A070939, A115623, A124736, A129129, A185974, A238966, A246867, A294648, A333483, A333484, A333485, A333486, A334433, A334434, A334435, A334436, A334437, A334438, A334440, A334441, A335123, A335124, A339195.
%K A344087 nonn,tabf
%O A344087 0,2
%A A344087 _Gus Wiseman_, May 11 2021