cp's OEIS Frontend

A358563 The number of maximal antichains in the Tamari lattice of order n.

%I A358563 #12 Jan 25 2023 09:54:46
%S A358563 1,2,4,26,1979,161117453
%N A358563 The number of maximal antichains in the Tamari lattice of order n.
%C A358563 Also the number of maximal order ideals in the Tamari lattice of order n.
%C A358563 Maximal antichains are those which cannot be extended without violating the antichain condition.
%D A358563 D. Tamari, The algebra of bracketings and their enumeration, Nieuw Archief voor Wiskunde, Series 3, 10 (1962), 131-146.
%H A358563 S. Huang and D. Tamari, <a href="https://doi.org/10.1016/0097-3165(72)90003-9">Problems of associativity: A simple proof for the lattice property of systems ordered by a semi-associative law</a>, J. of Comb. Theory, Series A, 13 (1972), 7-13.
%H A358563 Dmitry I. Ignatov, <a href="https://github.com/dimachine/TamariAnti">Supporting iPython code and input files for counting (maximal) antichains of the Tamari partition lattice up to n=5</a>, Github repository.
%H A358563 Wikipedia, <a href="http://en.wikipedia.org/wiki/Tamari_lattice">Tamari lattice</a>
%e A358563 The line (Hasse) diagram of the Tamari lattice for n=3 is
%e A358563      ((ab)c)d
%e A358563       /     \
%e A358563  (a(bc))d (ab)(cd)
%e A358563      |       /
%e A358563   a((bc)d)  /
%e A358563       \    /
%e A358563      a(b(cd))
%e A358563 with the a(3)=4 maximal antichains {((ab)c)d}, {(ab)(cd), (a(bc))d}, {(ab)(cd), a((bc)d)}, {a(b(cd))}.
%Y A358563 Cf. A358562 (number of antichains in the Tamari lattice).
%Y A358563 Cf. A326358 (number of maximal antichains in the Boolean lattice).
%Y A358563 Cf. A358041 (number of maximal antichains in the lattice of set partitions of an n-element set).
%Y A358563 Cf. A358390 (number of maximal antichains in the Kreweras lattice of non-crossing set partitions).
%Y A358563 Cf. A143674 (number of maximal antichains in the lattice of Dyck paths).
%K A358563 nonn,hard,more
%O A358563 1,2
%A A358563 _Dmitry I. Ignatov_, Nov 22 2022