
COMMENTS

Also the number of order ideals (downsets) for this poset.
This is the breakdown by size of (or number of elements in) the antichains beginning with antichains of size 0 and increasing:
n=0: 1, 1;
n=1: 1, 1;
n=2: 1, 2;
n=3: 1, 5, 1;
n=4: 1, 14, 21, 6;
n=5: 1, 42, 309, 793, 810, 348, 56, 2;
n=6: 1, 132, 4059, 54706, 390885, 1648100, 4380095, 7682096, 9172750, 7585779, 4370731, 1749626, 481189, 89055, 10676, 785, 38, 1;
Note that the number of maximum antichains (for each n) is given by the rightmost entry in each of these rows.


EXAMPLE

For n = 3 there are 7 antichains. Assume that the five elements in the D_3 poset are depicted using a Hasse diagram and labeled A through E from bottom to top. Then the 7 antichains are: { }, {A}, {B}, {C}, {D}, {E}, {B,C}.
