[seqfan] Permutation inverse = inversion

Ron Hardin rhhardin at att.net
Mon Aug 30 04:35:50 CEST 2010


A curiosity that just came up

1,0,0,2,2,0,0,12,12,0,0,120,120,0,0,1680,1680,0,0,30240,30240
Number of permutations of 1..n p(i) with inverse permutation q(i) equal to the 
inversion: q(i)=n+1-p(i)

eg. for n=8 the 12 permutations & inverses

 5 3 7 1 8 2 6 4 . 4 6 2 8 1 7 3 5 1
 5 6 2 1 8 7 3 4 . 4 3 7 8 1 2 6 5 1
 3 5 8 2 7 1 4 6 . 6 4 1 7 2 8 5 3 1
 3 4 8 7 2 1 5 6 . 6 5 1 2 7 8 4 3 1
 7 1 5 3 6 4 8 2 . 2 8 4 6 3 5 1 7 1
 7 1 4 6 3 5 8 2 . 2 8 5 3 6 4 1 7 1
 2 8 5 3 6 4 1 7 . 7 1 4 6 3 5 8 2 1
 2 8 4 6 3 5 1 7 . 7 1 5 3 6 4 8 2 1
 6 5 1 2 7 8 4 3 . 3 4 8 7 2 1 5 6 1
 6 4 1 7 2 8 5 3 . 3 5 8 2 7 1 4 6 1
 4 3 7 8 1 2 6 5 . 5 6 2 1 8 7 3 4 1
 4 6 2 8 1 7 3 5 . 5 3 7 1 8 2 6 4 1

the nonzero counts match

http://www.research.att.com/~njas/sequences/A001813
Quadruple factorial numbers: (2n)!/n!. 


 rhhardin at mindspring.com
rhhardin at att.net (either)






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