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The value set of polynomials over ℤm and the combinatorics of sequences

Part of:Finite fields and commutative rings (number-theoretic aspects)

Published online by Cambridge University Press:  26 February 2010

W. J. Ralph
W. J. Ralph
Affiliation:
Department of Mathematics, Brock University, St. Catharines, Ontario, Canada, L2S 3A1.
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Abstract

For a class of functions containing polynomials over ℤm, we give an inequality relating the cardinality of the value set to the additive order of differences of elements in that set. To do this, we find some inequalities concerning the combinatorics of substrings of sequences on finite sets which are related to an interesting matrix inequality.

MSC classification

Secondary:11T06: Polynomials

Information

Type
Research Article
Information
Mathematika , Volume 42 , Issue 1 , June 1995, pp. 190 - 198
Copyright
Copyright © University College London 1995

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