I am interested to know from basic to advance what is
PARITY of a permutation
I have searched about it but each time I got more confused.
I want to know the logic behind parity, like why is it required. This term is new to me and I have no knowledge about it, but I feel like this is the time to know it.
I don't know what are rotations and why they matter.
I came to know about this word when I was trying to find the number of permutions in $ n \times n \times n $ cube.
Please help me because this word is new to me. I would pefer any reading material on this topic for beginners. Thank you in advance.
The word "parity" means "evenness or oddness". Thus, if we speak of the parity of an integer, we mean whether the integer is even or odd, as in "The value of $(-1)^n$depends on the parity of $n."$ In the case of permutations, there is a theorem that says "Any permutation can be expressed as a product of finitely many transpositions. This decomposition is not unique but ,for any particular permuation, the number of such transpositions is either always even or always odd. " Thus it is legitimate to define "signum of a permutation $P=(-1)^n$ where $n$ is the number of transpositions when $P$ is written as a product of transpositions." When we speak of the "parity" of a permutation $P$, we mean whether the number of transpositions in a decomposition of $P$ into a product of transpositions is even or odd.