A344084 - OEIS

%I #11 Sep 22 2023 09:04:30

%S 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 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 3,4,5,2,3,4,5,1,2,3,4,5

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

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

%e The sets are the columns below:

%e   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       2   3 3 2   4 4 4 2 3 3 2   5 5 5 5 2 3 4 3 4 4 2

%e               3         4 4 4 3           5 5 5 5 5 5 3

%e                               4                       5

%e As a tetrangle, the first four triangles are:

%e   {1}

%e   {2},{1,2}

%e   {3},{1,3},{2,3},{1,2,3}

%e   {4},{1,4},{2,4},{3,4},{1,2,4},{1,3,4},{2,3,4},{1,2,3,4}

%t SortBy[Rest[Subsets[Range[5]]],Last]

%Y Triangle lengths are A000079.

%Y Triangle sums are A001793.

%Y Positions of first appearances are A005183.

%Y Set maxima are A070939.

%Y Set lengths are A124736.

%Y Cf. A005117, A014466, A209862.

%Y 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 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 nonn,tabf

%O 1,2

%A _Gus Wiseman_, May 11 2021