This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A384061 #12 May 22 2025 21:00:04
%S A384061 3,9,250,67595432
%N A384061 Number of antichains in the Bruhat order of type A_n.
%C A384061 The number of antichains in the Bruhat order of the Weyl group A_n (isomorphic to the symmetric group S_{n+1}).
%D A384061 A. Bjorner, F. Brenti, Combinatorics of Coxeter Groups, Springer, 2009, 27-64.
%D A384061 V. V. Deodhar, On Bruhat ordering and weight-lattice ordering for a Weyl group, Indagationes Mathematicae, vol. 81, 1 (1978), 423-435.
%e A384061 For n=1 the elements are 1 (identity) and s1, the order contains pair (1, s1). The antichains are {}, {1}, and {s1}.
%e A384061 For n=2 the line (Hasse) diagram is below.
%e A384061 s1*s2*s1
%e A384061 / \
%e A384061 s2*s1 s1*s2
%e A384061 | X |
%e A384061 s2 s1
%e A384061 \ /
%e A384061 1
%e A384061 The set of antichains is {{}, {1}, {s2}, {s2, s1}, {s1}, {s2*s1}, {s2*s1, s1*s2}, {s1*s2}, {s1*s2*s1}}.
%Y A384061 Cf. A000142 (the order size), A005130 (the size of Dedekind-MacNeille completion), A384062.
%K A384061 nonn,hard,more
%O A384061 1,1
%A A384061 _Dmitry I. Ignatov_, May 18 2025