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a(n) is the smallest number m such that any lattice having at least m elements must have a sublattice with exactly n elements.
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%I #9 Nov 10 2023 03:00:29

%S 1,2,3,4,5,6,9,8

%N a(n) is the smallest number m such that any lattice having at least m elements must have a sublattice with exactly n elements.

%C a(9) >= 17. For n >= 10, a(n) >= n + 2. a(n) <= n^(3n) for all n.

%D G. Gratzer, General Lattice Theory. Birkhäuser, Basel, 1998, 2nd edition, p. 72.

%K nonn,hard,more,nice

%O 1,2

%A _David Wasserman_, Mar 05 2002