71.56 ReverseDominance

ReverseDominance(mu, nu)

This is another total order on partitions which extends the dominance ordering (see Dominates). Here mu is greater than nu if for all i>0 sum_jge imu_j sum_jge inu_j.

gap> p:=Partitions(6);;Sort(p,ReverseDominance); p;
[ [ 6 ], [ 5, 1 ], [ 4, 2 ], [ 3, 3 ], [ 4, 1, 1 ], [ 3, 2, 1 ], 
  [ 2, 2, 2 ], [ 3, 1, 1, 1 ], [ 2, 2, 1, 1 ], [ 2, 1, 1, 1, 1 ], 
  [ 1, 1, 1, 1, 1, 1 ] ] 

This is the ordering used by James in the appendix of his Springer lecture notes book.

This function requires the package ``specht'' (see RequirePackage).

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