9/9/2023 0 Comments Define permutationI assume for example that in the list $(4,2,3,1)$ is the permutation mapping $1\mapsto 4$, $2\mapsto 2$, $3\mapsto 3$, $4\mapsto 1$? The usual (or cycle) notation for this would be $(1,4)$, an odd permutation.Īs you have written $(2,3,1,4)$, would usually be written $(1,2,3)=(1,2)(1,3)$ (or $(1,3)(1,2)$ depending on the convention you use), an even permutation. I haven't checked your list for completeness, but I suspect it does include all the permutations, you've just mixed up two different notations. There are twenty four elements in $\mathcal_n$.ĭon't be put off! You have made a very simple mistake which might be easily rectified. So in this case $(1,2,3,4)$ is even (no swaps)Īlso $(4,2,1,3)$ = Swap 34 then swap 14 = even permutation Also there is a swapping logic! If the numbers are swapped odd times then it is odd and even otherwise. I am confused here, is my solution incorrect? May be there will be more permutations with less elements like $(1,2,3), (1,2,4)$?
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