### Abstract

The well-known concept of a polynomial function (mod m) has been generalized to polynomial functions from Z_{n} to Z_{m}, and a number of results have been obtained in (Chen, 1995). In the present paper, we further define the concept of polynomial functions from Z_{n1} × Z_{n2} × ⋯ × Z_{nr} to Z_{m} and generalize the results of (Chen, 1995). We give a canonical representation and the counting formula for such polynomial functions. Then we obtain a necessary and sufficient condition on n_{1},n_{2}, ... , n_{r} and m for all functions from Z_{n1} × Z_{n2} × ⋯ × Z_{nr} to Z_{m} to be polynomial functions. Further, we give an answer to the following problem: How to determine whether a given function from Z_{n1} × Z_{n2} × ⋯ × Z_{nr} to Z_{m} is a polynomial function, and how to obtain a polynomial to represent a polynomial function from Z_{n1} × Z_{n2} × ⋯ × Z_{nr} to Z_{m}?

Original language | English (US) |
---|---|

Pages (from-to) | 67-76 |

Number of pages | 10 |

Journal | Discrete Mathematics |

Volume | 162 |

Issue number | 1-3 |

DOIs | |

State | Published - Dec 25 1996 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

## Fingerprint Dive into the research topics of 'On polynomial functions from Z<sub>n1</sub> × Z<sub>n2</sub> × ⋯ × Z<sub>nr</sub> to Z<sub>m</sub>'. Together they form a unique fingerprint.

## Cite this

_{n1}× Z

_{n2}× ⋯ × Z

_{nr}to Z

_{m}.

*Discrete Mathematics*,

*162*(1-3), 67-76. https://doi.org/10.1016/0012-365X(95)00305-G