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A NOTE ON INTERPOLATION OF PERMUTATIONS OF A SUBSET OF A FINITE FIELD

Published online by Cambridge University Press:  15 May 2014

CHRIS CASTILLO
Affiliation:
Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA
ROBERT S. COULTER*
Affiliation:
Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA email [email protected]
STEPHEN SMITH
Affiliation:
Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA
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Abstract

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We determine several variants of the classical interpolation formula for finite fields which produce polynomials that induce a desirable mapping on the nonspecified elements, and without increasing the number of terms in the formula. As a corollary, we classify those permutation polynomials over a finite field which are their own compositional inverse, extending work of C. Wells.

Type
Research Article
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

References

Carlitz, L., ‘A note on permutation functions over a finite field’, Duke Math. J. 29 (1962), 325332.Google Scholar
Dickson, L. E., ‘The analytic representation of substitutions on a power of a prime number of letters with a discussion of the linear group’, Ann. of Math. (2) 11 (1897), 65120; 161–183.CrossRefGoogle Scholar
Matthews, R., ‘Permutation properties of the polynomials 1 + x + ⋯ + x k over a finite field’, Proc. Amer. Math. Soc. 120 (1994), 4751.Google Scholar
Wells, C., ‘The degrees of permutation polynomials over finite fields’, J. Combin. Theory 7 (1969), 4955.Google Scholar
Wesselkamper, T. C., ‘The algebraic representation of partial functions’, Discrete Appl. Math. 1 (1979), 137142.Google Scholar
Zsigmondy, K., ‘Über wurzellose Congruenzen in Bezug auf einen Primzalmodul’, Monatsh. Math. Phys. 8 (1897), 142.Google Scholar