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A361952
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Array read by antidiagonals: T(n,k) is the number of unlabeled posets with n elements together with a function rk mapping each element to a rank between 1 and k such that whenever v covers w in the poset then rk(v) = rk(w) + 1.
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3
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1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 3, 4, 1, 0, 1, 4, 8, 8, 1, 0, 1, 5, 13, 21, 17, 1, 0, 1, 6, 19, 40, 58, 38, 1, 0, 1, 7, 26, 66, 126, 172, 94, 1, 0, 1, 8, 34, 100, 228, 420, 569, 258, 1, 0, 1, 9, 43, 143, 373, 816, 1537, 2148, 815, 1, 0, 1, 10, 53, 196, 571, 1412, 3140, 6342, 9538, 3038, 1, 0
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,8
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COMMENTS
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A poset is counted once for each admissible ranking function. This is an intermediate step in the computation of A361953 where each graded poset is counted exactly once.
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LINKS
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EXAMPLE
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Array begins:
============================================
n/k| 0 1 2 3 4 5 6 7 ...
---+----------------------------------------
0 | 1 1 1 1 1 1 1 1 ...
1 | 0 1 2 3 4 5 6 7 ...
2 | 0 1 4 8 13 19 26 34 ...
3 | 0 1 8 21 40 66 100 143 ...
4 | 0 1 17 58 126 228 373 571 ...
5 | 0 1 38 172 420 816 1412 2272 ...
6 | 0 1 94 569 1537 3140 5631 9351 ...
7 | 0 1 258 2148 6342 13383 24410 41097 ...
...
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PROG
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(PARI) \\ See Links in A361953 for program.
{ my(A=A361952tabl(7)); for(i=1, #A, print(A[i, ])) }
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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