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A143674 Number of maximal antichains in the poset of Dyck paths ordered by inclusion. 2
1, 1, 2, 4, 17, 379, 526913 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=0..6.

J. Woodcock, Properties of the poset of Dyck paths ordered by inclusion

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: A048872 A063800 A207137 * A136147 A275837 A119510

Adjacent sequences:  A143671 A143672 A143673 * A143675 A143676 A143677

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

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Last modified January 21 05:23 EST 2020. Contains 331104 sequences. (Running on oeis4.)