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A263864 Triangle read by rows: T(n,k) (n>=1, k>=1) is the number of posets with n elements whose Hasse diagram has k connected components. 7

%I #26 Sep 04 2022 17:02:11

%S 1,1,1,3,1,1,10,4,1,1,44,13,4,1,1,238,60,14,4,1,1,1650,312,63,14,4,1,

%T 1,14512,2075,328,64,14,4,1,1,163341,17316,2159,331,64,14,4,1,1,

%U 2360719,186173,17801,2175,332,64,14,4,1,1,43944974,2594568,189406,17885,2178,332,64,14,4,1,1,1055019099,47041877

%N Triangle read by rows: T(n,k) (n>=1, k>=1) is the number of posets with n elements whose Hasse diagram has k connected components.

%C Multiset transformation of A000608.

%H Alois P. Heinz, <a href="/A263864/b263864.txt">Rows n = 1..16, flattened</a>

%H FindStat - Combinatorial Statistic Finder, <a href="http://www.findstat.org/StatisticsDatabase/St000181">The number of connected components of the Hasse diagram for the poset</a>.

%H Salah Uddin Mohammad, Md. Shah Noor, and Md. Rashed Talukder, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL25/Uddin/uddin6.html">An Exact Enumeration of the Unlabeled Disconnected Posets</a>, J. Int. Seq., Vol. 25 (2022), Article 22.5.4.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Hasse_diagram">Hasse diagram</a>

%H <a href="/index/Pos#posets">Index entries for sequences related to posets</a>

%e Triangle begins:

%e 1;

%e 1, 1;

%e 3, 1, 1;

%e 10, 4, 1, 1;

%e 44, 13, 4, 1, 1;

%e ...

%Y Cf. A000112 (row sums), A000608 (k=1).

%K nonn,tabl

%O 1,4

%A _Christian Stump_, Oct 28 2015

%E More terms from _R. J. Mathar_, Jul 12 2020

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Last modified March 19 01:57 EDT 2024. Contains 370952 sequences. (Running on oeis4.)