On a Frobenius problem for polynomials

Ricardo Conceição; Rodrigo Gondim; Miguel Rodriguez

On a Frobenius problem for polynomials

Number Theory 2014-09-16 v1

Authors: Ricardo Conceição , Rodrigo Gondim , Miguel Rodriguez

Abstract

We extend the famous diophantine Frobenius problem to the case of polynomials over a field $k$ . Similar to the classical problem, we show that the $n=2$ case of the Frobenius problem for polynomials is easy to solve. In addition, we translate a few results from the Frobenius problem over $\mathbb{Z}$ to $k[t]$ and give an algorithm to solve the Frobenius problem for polynomials over a field $k$ of sufficiently large size.

Keywords

polynomials over finite fields frobenius algebra polynomial theory

Cite

@article{arxiv.1409.4129,
  title  = {On a Frobenius problem for polynomials},
  author = {Ricardo Conceição and Rodrigo Gondim and Miguel Rodriguez},
  journal= {arXiv preprint arXiv:1409.4129},
  year   = {2014}
}

Comments

22 pages, submitted

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