The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A143673 Number of antichains in the poset of Dyck paths ordered by inclusion. 4
2, 2, 3, 7, 42, 2361, 37620704 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
Also the number of order ideals (down-sets) 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.
REFERENCES
R. P. Stanley, Enumerative Combinatorics 1, Cambridge University Press, New York, 1997.
LINKS
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}.
CROSSREFS
Cf. A143672. Number of maximal antichains A143674.
Sequence in context: A052449 A053413 A232542 * A089543 A139073 A329955
KEYWORD
nonn,more
AUTHOR
Jennifer Woodcock (jennifer.woodcock(AT)ugdsb.on.ca), Aug 28 2008
EXTENSIONS
a(6) from Alois P. Heinz, Jul 28 2011
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 20 03:57 EDT 2024. Contains 372703 sequences. (Running on oeis4.)