Re: [math-fun] Characterizing polys which permute GF(p)

Generated only the *alternating* subgroup. Let e(i)(x)=1-(x-i)^(p-1). This poly function e(i) over x maps i->1, everything else to 0. Then r(x)=2*e(0)-e(1)-e(2)+x does a rotation of 0,1,2, leaving the other elements stationary. By construction, r(x) is divisible by (x-1), since r(1)=0. {x,x+1,2*e(0)-e(1)-e(2)+x} generates the *alternating group* (group of even perms), for every odd prime p. By one of Dickson's theorems, r(x) is a Dickson/Chebyshev poly, but I haven't figured out which one yet. BTW, has anyone figured out the intuition behind why the Dickson (perm) polys are the Chebyshev polys ?