|
|
A342447
|
|
T(n,e) is the number of unlabeled posets of n>=0 points with e>=0 arcs in the Hasse diagram, irregular triangle read by rows.
|
|
6
|
|
|
1, 1, 1, 1, 1, 1, 3, 1, 1, 4, 8, 2, 1, 1, 4, 11, 29, 12, 5, 1, 1, 4, 12, 43, 105, 92, 45, 12, 3, 1, 1, 4, 12, 46, 156, 460, 582, 487, 204, 71, 14, 7, 1, 1, 4, 12, 47, 170, 670, 2097, 3822, 4514, 3271, 1579, 561, 186, 44, 16, 4, 1, 1, 4, 12, 47, 173, 731, 2954, 10513, 24584, 40182
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,7
|
|
REFERENCES
|
Maximal e for a given n (i.e., the length of the n-th row minus 1) is no less than A002620(n) and possibly equals that value. - Andrey Zabolotskiy, Mar 12 2021
|
|
LINKS
|
Brendan McKay, Digraphs, posets tables at the bottom of the page.
|
|
FORMULA
|
T(n,0) = T(n,1) = 1.
|
|
EXAMPLE
|
The table starts
1 ;
1 ;
1 1 ;
1 1 3 ;
1 1 4 8 2 ;
1 1 4 11 29 12 5 ;
1 1 4 12 43 105 92 45 12 3 ;
1 1 4 12 46 156 460 582 487 204 71 14 7 ;
1 1 4 12 47 170 670 2097 3822 4514 3271 1579 561 186 44 16 4 ;
...
T(4,0) = 1: the 4-point poset with no relations, 4 isolated points in the Hasse diagram.
T(4,1) = 1: the 4-point poset with one relation, the Hasse diagram has one vertical line and 2 isolated points.
T(4,2) = 4: the 4 posets contributing to A022016(4) = 4, extended by additional isolated point when the number of points is less than 4.
T(4,3) = 8: the 8 posets contributing to A022017(3).
T(4,4) = 2: the "dagaz rune" poset {1<3, 2<3, 1<4, 2<4}
o o
|X|
o o
and the "diamond" poset {1<2, 1<3, 2<4, 3<4}
o
/ \
o o
\ /
o
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,tabf,hard
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|