cp's OEIS Frontend

A344084 Concatenated list of all finite nonempty sets of positive integers sorted first by maximum, then by length, and finally lexicographically.

%I A344084 #11 Sep 22 2023 09:04:30
%S A344084 1,2,1,2,3,1,3,2,3,1,2,3,4,1,4,2,4,3,4,1,2,4,1,3,4,2,3,4,1,2,3,4,5,1,
%T A344084 5,2,5,3,5,4,5,1,2,5,1,3,5,1,4,5,2,3,5,2,4,5,3,4,5,1,2,3,5,1,2,4,5,1,
%U A344084 3,4,5,2,3,4,5,1,2,3,4,5
%N A344084 Concatenated list of all finite nonempty sets of positive integers sorted first by maximum, then by length, and finally lexicographically.
%H A344084 Wikiversity, <a href="https://en.wikiversity.org/wiki/Lexicographic_and_colexicographic_order">Lexicographic and colexicographic order</a>
%e A344084 The sets are the columns below:
%e A344084   1 2 1 3 1 2 1 4 1 2 3 1 1 2 1 5 1 2 3 4 1 1 1 2 2 3 1
%e A344084       2   3 3 2   4 4 4 2 3 3 2   5 5 5 5 2 3 4 3 4 4 2
%e A344084               3         4 4 4 3           5 5 5 5 5 5 3
%e A344084                               4                       5
%e A344084 As a tetrangle, the first four triangles are:
%e A344084   {1}
%e A344084   {2},{1,2}
%e A344084   {3},{1,3},{2,3},{1,2,3}
%e A344084   {4},{1,4},{2,4},{3,4},{1,2,4},{1,3,4},{2,3,4},{1,2,3,4}
%t A344084 SortBy[Rest[Subsets[Range[5]]],Last]
%Y A344084 Triangle lengths are A000079.
%Y A344084 Triangle sums are A001793.
%Y A344084 Positions of first appearances are A005183.
%Y A344084 Set maxima are A070939.
%Y A344084 Set lengths are A124736.
%Y A344084 Cf. A005117, A014466, A209862.
%Y A344084 Partition/composition orderings: A026791, A026792, A026793, A036036, A036037, A048793, A066099, A080577, A112798, A118457, A124734, A162247, A193073, A211992, A228100, A228531, A246688, A272020, A296774, A299755, A304038, A319247, A329631, A334301, A334302, A334439, A334442, A335122, A344085, A344086, A344087, A344088, A344089.
%Y A344084 Partition/composition applications: A036043, A049085, A115623, A129129, A185974, A238966, A294648, A333483, A333484, A333485, A333486, A334433, A334434, A334435, A334436, A334437, A334438, A334440, A334441, A335123, A335124, A339195.
%K A344084 nonn,tabf
%O A344084 1,2
%A A344084 _Gus Wiseman_, May 11 2021