Affinity of permutations of image Original Research Article

It was conjectured that if n is even, then every permutation of image is affine on some 2-dimensional affine subspace of image. We prove that the conjecture is true for image, for quadratic permutations of image and for permutation polynomials of image with coefficients in image. The conjecture is actually a claim about image-double cosets in permutation group image of image. We give a formula for the number of image-double cosets in image and classify the image-double cosets in image.