Permutations & Polynomials

[Olivier Gerard]

Applying Lagrange interpolation to all permutations
(but it is better to use   0..n-1 as labels)
will lead you to classical groups.

For  n a prime all coefficients are integers (in
reality elements of a Galois Field) if you work modulo n.
Many authors of the XIXth century used to refer or
define permutations by a polynomial.

On 4/1/06, zak seidov <zakseidov at yahoo.com> wrote:
> In general, a(i)=A+B*i +C*i^2+D*i^3, and we can find
> coefficients of polynomials for all 24 permutations: