Question: why does setting each xi equal to 2 in the cycle structure representation of a symmetry count the number of 2-colorings of a square left

why does setting each xi equal to 2 in the cycle structure representation of a symmetry count the number of 2-colorings of a square left by

when does the Augmenting Flow Algorithm terminate with no more iterations of the Algorithm possible?

why are the positions Grundy value 0 the kernel of the game?

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