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 A382346 #11 May 29 2025 15:46:01
%S A382346 3,12,2247
%N A382346 Number of antichains in the Bruhat order on B_n.
%C A382346 The number of antichains in the Bruhat order of the Weyl group B_n (the hyperoctahedral group).
%D A382346 A. Bjorner and F. Brenti, Combinatorics of Coxeter Groups, Springer, 2009, 27-64.
%H A382346 V. V. Deodhar, <a href="https://doi.org/10.1016/1385-7258(78)90059-8">On Bruhat ordering and weight-lattice ordering for a Weyl group</a>, Indagationes Mathematicae, vol. 81, 1 (1978), 423-435.
%e A382346 For n=1 the elements are 1 (identity) and s1, the order contains pair (1, s1). The antichains are {}, {1}, and {s1}.
%e A382346 For n=2 the line (Hasse) diagram is below.
%e A382346 s2*s1*s2*s1
%e A382346 / \
%e A382346 s2*s1*s2 s1*s2*s1
%e A382346 | X |
%e A382346 s2*s1 s1*s2
%e A382346 | X |
%e A382346 s2 s1
%e A382346 \ /
%e A382346 1
%e A382346 The set of antichains is {{}, {1}, {s2}, {s2, s1}, {s1}, {s2*s1}, {s2*s1, s1*s2}, {s1*s2}, {s2*s1*s2}, {s2*s1*s2, s1*s2*s1}, {s1*s2*s1}, {s2*s1*s2*s1}}.
%Y A382346 Cf. A005900 (the number of join-irreducible elements), A378072 (the size of Dedekind-MacNeille completion).
%K A382346 nonn,hard,more,bref
%O A382346 1,1
%A A382346 _Dmitry I. Ignatov_, May 18 2025