A363232
Triangular array read by rows. T(n,k) is the number of idempotent Boolean relation matrices with rank k, n >= 0, 0 <= k <= n.
Original entry on oeis.org
1, 1, 1, 1, 7, 3, 1, 37, 66, 19, 1, 175, 975, 990, 219, 1, 781, 12090, 32575, 23345, 4231, 1, 3367, 135903, 866550, 1514610, 814903, 130023
Offset: 0
Triangle begins:
1;
1, 1;
1, 7, 3;
1, 37, 66, 19;
1, 175, 975, 990, 219;
1, 781, 12090, 32575, 23345, 4231;
1, 3367, 135903, 866550, 1514610, 814903, 130023;
...
A363911
n! times the number of posets with n unlabeled elements.
Original entry on oeis.org
1, 1, 4, 30, 384, 7560, 228960, 10306800, 685399680, 66490865280, 9316160179200, 1866087527673600, 529244914160793600, 210621677079215001600, 116661392964364363315200, 89281569344544938769408000, 93799600948326479830880256000
Offset: 0
-
nn = 10; A000112 = Cases[Import["https://oeis.org/A000112/b000112.txt",
"Table"], {, }][[All, 2]];Range[0, 16]! Table[A000112[[i]], {i, 1, 17}]
A366396
Number of labeled directed graphs on [n] with self loops allowed such that the following implication holds for all x,y in [n]. If x and y are in distinct strongly connected components and y is reachable from x then there is a directed edge from x to y.
Original entry on oeis.org
1, 2, 16, 368, 34624, 19194752, 47730489856, 452968293106688, 16282682505688059904, 2253889950034687424110592, 1219139359408849690950674415616, 2601990460616856808147727573494857728, 22041041736721298233193355574294486210576384
Offset: 0
-
nn = 12; posets = Select[Import["https://oeis.org/A001035/b001035.txt", "Table"],
Length@# == 2 &][[All, 2]];p[x_] := Total[posets Table[x^i/i!, {i, 0, 18}]]; strong = Select[Import["https://oeis.org/A003030/b003030.txt", "Table"],
Length@# == 2 &][[All, 2]]; s[x_] := Total[Prepend[strong Table[x^i/i!, {i, 1, 58}], 1]];Table[n!, {n, 0, nn}] CoefficientList[Series[p[s[2 x] - 1], {x, 0, nn}], x]
A366705
Number of symmetry classes of partially ordered pattern classes defined by avoiding a size n poset.
Original entry on oeis.org
1, 1, 2, 7, 64, 1068, 32651
Offset: 0
There are three labeled posets with 2 elements. The two chains generate symmetrically equivalent permutation classes, Av(12) and Av(21), while the third generates Av(12, 21) which is not equivalent to these. Therefore a(2) = 2.
- Christian Bean, Émile Nadeau, Jay Pantone, and Henning Ulfarsson, Permutations avoiding bipartite partially ordered patterns have a regular insertion encoding, The Electronic Journal of Combinatorics, Volume 31, Issue 3 (2024); arXiv preprint, arXiv:2312.07716 [math.CO], 2023.
- Alice L. L. Gao and Sergey Kitaev, On partially ordered patterns of length 4 and 5 in permutations, arXiv:1903.08946 [math.CO], 2019.
- Alice L. L. Gao and Sergey Kitaev, On partially ordered patterns of length 4 and 5 in permutations, The Electronic Journal of Combinatorics 26(3) (2019), P3.26.
A376064
Number of quasi-orders on an n-set that are not partial orders.
Original entry on oeis.org
0, 0, 1, 10, 136, 2711, 79504, 3405382, 211055975, 18749246912, 2365988624260, 420564361630293, 104490620009920522, 36030665275081893690, 17132727719926060775277, 11169098098145556139435182, 9930583626219881751366237516, 11985408843042557809380587456695, 19553143146433198202168306753032180
Offset: 0
-
a[n_]:=Part[ResourceFunction["OEISSequence"]["A000798"],n+1]-Part[ResourceFunction["OEISSequence"]["A001035"],n+1]; Array[a,18,0] (* Stefano Spezia, Sep 08 2024 *)
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