Even Permutation
An even permutation is a permutation obtainable from an even number of two-element swaps, i.e., a permutation
with permutation symbol equal to 
. For initial
set 
1,2,3,4
, the twelve even
permutations are those with zero swaps: (
1,2,3,4
); and those with
two swaps: (
1,3,4,2
, 
1,4,2,3
, 
2,1,4,3
, 
2,3,1,4
, 
2,4,3,1
, 
3,1,2,4
, 
3,2,4,1
, 
3,4,1,2
, 
4,1,3,2
, 
4,2,1,3
, 
4,3,2,1
).
For a set of 
elements and 
, there are
even permutations, which is the same as the
number of odd permutations. For 
, 2, ..., the
numbers are given by 0, 1, 3, 12, 60, 360, 2520, 20160, 181440, ... (OEIS A001710).
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even permutation
