Every function from a finite field to itself can be represented by a polynomial. The functions which are also permutations give rise to "permutation polynomials," which have potential applications in cryptology. We will introduce a generalization of permutation polynomials called ``degree-preserving polynomials" and show a classification scheme of the latter. The criteria for a polynomial to qualify as degree preserving are certainly less stringent than those for the permuting qualification. Thus the idea to study degree-preserving polynomials allows more opportunity to maneuver and gain intuition about the occurrence of such polynomials.

Author Bio

Dylan Cutler is a math major at Middlebury College. Hailing from western Massachusetts, he enjoys being outdoors, geology and of course math.

Jesse Johnson graduated from Middlebury in 2002 and is now a graduate student in mathematics at The University of California at Davis.

Ben Rosenfield is a senior math major at Middlebury College and enjoys the culinary arts.

Kudzai Zvoma is a math major at Middlebury, who hopes to persue a career in education.