Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-27T21:50:00.317Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Bremser, P. and Gomez Calderon, J.. Value sets of Dickson polynomials over Galois rings. J. of Number Theory, 38 (1991), 240–250.CrossRefGoogle Scholar
2.Carlitz, L., Lewis, D. J., Mills, W. H. and Strauss, E. G.. Polynomials over finite fields with minimal value sets. Mathematika, 8 (1961), 121–130.CrossRefGoogle Scholar
3.Chou, W. S., Gomez Calderon, J. and Mullen, G. L.. Value sets of Dickson polynomials over finite fields. J. of Number Theory, 30 (1988), 334–344.CrossRefGoogle Scholar
4.Dickson, L.. History of the theory of numbers (Chelsea Publishing Company, New York, 1952).Google Scholar
5.Gomez Calderon, J.. A note on polynomials with minimal value set over finite fields. Mathematika, 35 (1988), 144–148.CrossRefGoogle Scholar
6.Lidl, R. and Niederreiter, H.. Introduction to finite fields and their applications (Cambridge University Press, 1986).Google Scholar
7.Nagell, T.. Introduction to number theory (Chelsea Publishing Company, New York, 1964).Google Scholar