A077765 Number of maximum-size antichains in partition lattice Par(n).

1, 1, 2, 3, 5, 7, 2, 4, 15, 4, 2, 11, 18, 14, 53, 2, 54, 1606, 482, 104, 754, 536

Offset: 0

Author

Dean Hickerson, Nov 14 2002

Keywords

• nonn
• more

Comments

Par(n) is the set of partitions of n under 'dominance order': partition P is <= partition Q iff the sum of the largest k parts of P is <= the corresponding sum for Q for all k.

Examples

			For n=10, the maximum size is A076269(10)=4. There are 2 maximum-size antichains: {5+1+1+1+1+1, 4+3+1+1+1, 4+2+2+2, 3+3+3+1} and {6+1+1+1+1, 5+2+2+1, 4+4+1+1, 4+3+3}. So a(10)=2.
		

Crossrefs

The corresponding sizes are in A076269.

Programs

Mathematica

leq[p_, q_] := If[Length[p]