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A143674
Number of maximal antichains in the poset of Dyck paths ordered by inclusion.
3
1, 1, 2, 4, 17, 379, 526913
OFFSET
0,3
COMMENTS
Maximal antichains are those which cannot be extended without violating the antichain condition.
This is the breakdown by size of (or number of elements in) the antichains beginning with antichains of size 0 and increasing:
n=0: 0, 1;
n=1: 0, 1;
n=2: 0, 2;
n=3: 0, 3, 1;
n=4: 0, 3, 8, 6;
n=5: 0, 3, 14, 62, 132, 124, 42, 2;
n=6: 0, 3, 21, 157, 983, 4438, 15454, 41827, 79454, 112344, 117259, 88915, 47295, 14909, 3498, 334, 21, 1
REFERENCES
R. P. Stanley, Enumerative Combinatorics 1, Cambridge University Press, New York, 1997.
EXAMPLE
For n = 3 there are 4 maximal 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 4 maximal antichains are {A}, {B,C}, {D}, {E}.
CROSSREFS
Cf. A143672. Total number of antichains A143673.
Sequence in context: A063800 A207137 A355464 * A136147 A275837 A119510
KEYWORD
nonn,more
AUTHOR
Jennifer Woodcock (jennifer.woodcock(AT)ugdsb.on.ca), Aug 28 2008
EXTENSIONS
a(6) from Alois P. Heinz, Jul 31 2011
STATUS
approved