A358562 The number of antichains in the Tamari lattice of order n.
2, 3, 8, 83, 28984, 138832442543
Offset: 1
Examples
For n=3 the a(3)=8 antichains are {}, {((ab)c)d}, {(ab)(cd)}, {(a(bc))d}, {(ab)(cd), (a(bc))d}, {a((bc)d)}, {(ab)(cd), a((bc)d)}, {a(b(cd))}.
References
- D. Tamari, The algebra of bracketings and their enumeration, Nieuw Archief voor Wiskunde, Series 3, 10 (1962), 131-146.
Links
- S. Huang and D. Tamari, Problems of associativity: A simple proof for the lattice property of systems ordered by a semi-associative law, J. of Comb. Theory, Series A, 13 (1972), 7-13.
- Dmitry I. Ignatov, Supporting iPython code and input files for counting (maximal) antichains of the Tamari partition lattice up to n=6, Github repository.
- Wikipedia, Tamari lattice
Crossrefs
Cf. A000372 (number of antichains in the Boolean lattice).
Cf. A302250 (number of antichains in the lattice of set partitions).
Cf. A358391 (number of antichains in the Kreweras lattice of non-crossing set partitions of an n-element set).
Cf. A143673 (number of antichains in the lattice of Dyck paths).
Cf. A027686.
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