6.1 2314, 2431, 3241, 1342, 3124, 4132, 4213, 1423, 2143, 3412, 4321.

6.2 Image, because every such function partitions its domain into k nonempty subsets, and there are mk ways to assign function values for each partition. (Summing over k gives a combinatorial proof of (6.10).)

6.3 Now dk+1 (center of gravity) Image = 1 Image + (d1 + · · · + dk)/k. This recurrence is like (6.55) but with 1 in place of 1; hence the optimum solution is dk+1 = (1 )Hk. This ...

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