On polynomial functions from Zn to Zm

Zhibo Chen

doi:10.1016/0012-365X(93)E0162-W

On polynomial functions from Z_n to Z_m

Zhibo Chen

Penn State Greater Allegheny

Research output: Contribution to journal › Article › peer-review

27 Scopus citations

Abstract

We define the concept of a polynomial function from Z_n to Z_m, which is a generalization of the well-known polynomial function from Z_n to Z_m. We obtain a necessary and sufficient condition on n and m for all functions from Z_n to Z_m to be polynomial functions. Then we present canonical representations and the counting formula for the polynomial functions from Z_n to Z_m. Further, we give an answer to the following problem: How to determine whether a given function from Z_n to Z_m is a polynomial function, and how to obtain a polynomial to represent a polynomial function?

Original language	English (US)
Pages (from-to)	137-145
Number of pages	9
Journal	Discrete Mathematics
Volume	137
Issue number	1-3
DOIs	https://doi.org/10.1016/0012-365X(93)E0162-W
State	Published - Jan 20 1995

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/0012-365X(93)E0162-W

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abstract = "We define the concept of a polynomial function from Zn to Zm, which is a generalization of the well-known polynomial function from Zn to Zm. We obtain a necessary and sufficient condition on n and m for all functions from Zn to Zm to be polynomial functions. Then we present canonical representations and the counting formula for the polynomial functions from Zn to Zm. Further, we give an answer to the following problem: How to determine whether a given function from Zn to Zm is a polynomial function, and how to obtain a polynomial to represent a polynomial function?",

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AB - We define the concept of a polynomial function from Zn to Zm, which is a generalization of the well-known polynomial function from Zn to Zm. We obtain a necessary and sufficient condition on n and m for all functions from Zn to Zm to be polynomial functions. Then we present canonical representations and the counting formula for the polynomial functions from Zn to Zm. Further, we give an answer to the following problem: How to determine whether a given function from Zn to Zm is a polynomial function, and how to obtain a polynomial to represent a polynomial function?

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On polynomial functions from Z_n to Z_m

Abstract

All Science Journal Classification (ASJC) codes

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