Which Permutations Should Be Excluded in Leibniz Formula for Determinant?

[Amer]

Hey
libniz formula
i can't post picture and i can't use latex :(

if we want to use Libniz forumla for find the determinant of A such that

A = 1..-1..0..3
...2..-3..0..4
...0..2..-1..5
...1..2..2..3

sigma here from S_4 which has 4! elements which element will we choose

 

[Evgeny.Makarov]

We must exclude permutations which map 1 to 3 or 2 to 3 or 3 to 1. Suppose 1 is mapped to 1. Then 2 is mapped to 2 or 4. Therefore, the permutations that start with 1 are (1, 2, 3, 4), (1, 2, 4, 3), (1, 4, 2, 3) and (1, 4, 3, 2). Now try to come up with the remaining 6 permutations.