[seqfan] Re: Permutation inverse = inversion

Ron Hardin rhhardin at att.net
Mon Aug 30 13:46:47 CEST 2010






----- Original Message ----
> From: Ron Hardin <rhhardin at att.net>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Sent: Mon, August 30, 2010 6:32:29 AM
> Subject: [seqfan] Re: Permutation inverse = inversion
> 
> Ignoring the bug off-the-array trailing 1, the inverse and inversion is
> also  the reverse, which may be the key.

I wonder if these permutations are those 
with 90 degree rotational symmerty..

0: 5 3 7 1 8 2 6 4   4 6 2 8 1 7 3 5
 + + + X + + + +
 + + + + + X + +
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 X + + + + + + +
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1: 5 6 2 1 8 7 3 4   4 3 7 8 1 2 6 5
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 + + + + + + X +
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 X + + + + + + +
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 + + + + + X + +
 + + + + X + + +
2: 3 5 8 2 7 1 4 6   6 4 1 7 2 8 5 3
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 X + + + + + + +
 + + + + + + X +
 + X + + + + + +
 + + + + + + + X
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 + + X + + + + +
3: 3 4 8 7 2 1 5 6   6 5 1 2 7 8 4 3
 + + + + + X + +
 + + + + X + + +
 X + + + + + + +
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 + + + + + + X +
 + + + + + + + X
 + + + X + + + +
 + + X + + + + +
4: 7 1 5 3 6 4 8 2   2 8 4 6 3 5 1 7
 + X + + + + + +
 + + + + + + + X
 + + + X + + + +
 + + + + + X + +
 + + X + + + + +
 + + + + X + + +
 X + + + + + + +
 + + + + + + X +
5: 7 1 4 6 3 5 8 2   2 8 5 3 6 4 1 7
 + X + + + + + +
 + + + + + + + X
 + + + + X + + +
 + + X + + + + +
 + + + + + X + +
 + + + X + + + +
 X + + + + + + +
 + + + + + + X +
6: 2 8 5 3 6 4 1 7   7 1 4 6 3 5 8 2
 + + + + + + X +
 X + + + + + + +
 + + + X + + + +
 + + + + + X + +
 + + X + + + + +
 + + + + X + + +
 + + + + + + + X
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7: 2 8 4 6 3 5 1 7   7 1 5 3 6 4 8 2
 + + + + + + X +
 X + + + + + + +
 + + + + X + + +
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 + + + + + X + +
 + + + X + + + +
 + + + + + + + X
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8: 6 5 1 2 7 8 4 3   3 4 8 7 2 1 5 6
 + + X + + + + +
 + + + X + + + +
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 + + + + + + X +
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 X + + + + + + +
 + + + + X + + +
 + + + + + X + +
9: 6 4 1 7 2 8 5 3   3 5 8 2 7 1 4 6
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 + + + + X + + +
 + + + + + + + X
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 + + + + + + X +
 X + + + + + + +
 + + + X + + + +
 + + + + + X + +
10: 4 3 7 8 1 2 6 5   5 6 2 1 8 7 3 4
 + + + + X + + +
 + + + + + X + +
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 X + + + + + + +
 + + + + + + + X
 + + + + + + X +
 + + X + + + + +
 + + + X + + + +
11: 4 6 2 8 1 7 3 5   5 3 7 1 8 2 6 4
 + + + + X + + +
 + + X + + + + +
 + + + + + + X +
 X + + + + + + +
 + + + + + + + X
 + X + + + + + +
 + + + + + X + +
 + + + X + + + +





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