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On Value Sets of Polynomials over a Finite Field

โœ Scribed by Wayne Aitken

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
254 KB
Volume
4
Category
Article
ISSN
1071-5797

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โœฆ Synopsis

We study value sets of polynomials over a finite field, and value sets associated to pairs of such polynomials. For example, we show that the value sets (counting multiplicities) of two polynomials of degree at most d are identical or have at most q!(q!1)/d values in common where q is the number of elements in the finite field. This generalizes a theorem of D. Wan concerning the size of a single value set. We generalize our result to pairs of value sets obtained by restricting the domain to certain subsets of the field. These results are preceded by results concerning symmetric expressions (of low degree) of the value set of a polynomial. K. S. Williams, D. Wan, and others have considered such expressions in the context of symmetric polynomials, but we consider (multivariable) polynomials invariant under certain important subgroups of the full symmetry group.

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