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Number of maximum-diversity partitions of n.
2

%I #10 Apr 16 2015 07:13:01

%S 1,1,2,1,1,1,2,1,1,2,1,1,1,1,1,2,1,3,1,1,1,2,1,1,2,1,1,1,1,1,1,1,1,1,

%T 1,1,1,1,1,1,1,1,1,1,1,1,1,1,3,1,1,1,2,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,

%U 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1

%N Number of maximum-diversity partitions of n.

%C A maximum-diversity partition of n is an integer partition whose part distribution maximizes the number of different compositions (=distinct partition orderings) that can be constructed from it.

%C An integer composition of n corresponds to a subgroup of the symmetric group on n element whose cycles are formed of contiguous integers.

%H Alois P. Heinz, <a href="/A198254/b198254.txt">Table of n, a(n) for n = 0..1000</a>

%e For n=17, there are 3 partitions reaching the maximum possible of 7!/2 =2520 distinct orderings : {4, 3, 2, 2, 2, 1, 1, 1, 1}, {4, 3, 2, 2, 1, 1, 1, 1, 1, 1} and {3, 3, 2, 2, 2, 1, 1, 1, 1, 1}.

%Y A102462 gives the number of compositions that can be constructed from a maximum-diversity partition of n.

%Y Cf. A007294, A072811, A080575.

%K nonn,nice

%O 0,3

%A _Olivier GĂ©rard_, Oct 22 2011