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A384061

Number of antichains in the Bruhat order of type A_n.

3, 9, 250, 67595432

OFFSET

1,1

COMMENTS

The number of antichains in the Bruhat order of the Weyl group A_n (isomorphic to the symmetric group S_{n+1}).

REFERENCES

A. Bjorner and F. Brenti, Combinatorics of Coxeter Groups, Springer, 2009, 27-64.

LINKS

V. V. Deodhar, On Bruhat ordering and weight-lattice ordering for a Weyl group, Indagationes Mathematicae, vol. 81, 1 (1978), 423-435.

EXAMPLE

For n=1 the elements are 1 (identity) and s1, the order contains pair (1, s1). The antichains are {}, {1}, and {s1}.

For n=2 the line (Hasse) diagram is below.

s1*s2*s1

/ \

s2*s1 s1*s2

| X |

s2 s1

\ /

The set of antichains is {{}, {1}, {s2}, {s2, s1}, {s1}, {s2*s1}, {s2*s1, s1*s2}, {s1*s2}, {s1*s2*s1}}.

CROSSREFS

Cf. A000142 (the order size), A005130 (the size of Dedekind-MacNeille completion), A384062.

KEYWORD

nonn,hard,more

AUTHOR

STATUS

approved

URL: https://oeis.org/A384061