I want to add something to the 3-symmetric permutations of size 9. I have calculated the distance of all permutation of size 9 from the 3-symmetric status.

I used the variance to measure it. Of course the two 3-simmetric permutation have variance equal to zero. I searched which are the most distant from them, and

found out that they are [1, 2, 3, 4, 5, 6, 7, 8, 9] and [9, 8, 7, 6, 5, 4, 3, 2, 1] with a variance of 980. All the other permutations have intermediate variance from 0 to 980 and the most numerous group has 2328 elements with variance = 35.67. Both, the distribution of variances and the elements of each group are very

irregular. (the previous comment has a calculation error).

Excuse for my poor english, but my mother language is italian.

Thank you in advance.

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