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%I #33 Nov 19 2024 02:19:19
%S 1,2,10,132,4824,493600
%N Number of elements in the completion of the Bruhat order on B_n.
%C Lascoux and Schützenberger have shown that the completion of type B Bruhat order is distributive, and have described its irreducible elements. It follows that a(n) is the number of antichains in the poset of irreducible elements of the Bruhat order on B_n.
%C This sequence is a type B analog of A005130, since ASMs form a lattice isomorphic to the completion of type A Bruhat order.
%H A. Lascoux and M.-P. Schützenberger, <a href="https://doi.org/10.37236/1285">Treillis et bases des groupes de Coxeter</a>, Electron. J. Combin. 3 (1996), #R27.
%Y Cf. A005130 (ASMs), A005158 (centrally symmetric ASMs), A000165 (number of elements in B_n).
%K nonn,more
%O 0,2
%A _Ludovic Schwob_, Nov 16 2024