Rocky Mountain Journal of Mathematics

On a Frobenius problem for polynomials

R. Conceição, R. Gondim, and M. Rodriguez

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Abstract

We extend the famous diophantine Frobenius problem to a ring 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.

Article information

Source
Rocky Mountain J. Math., Volume 47, Number 5 (2017), 1427-1462.

Dates
First available in Project Euclid: 22 September 2017

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1506045620

Digital Object Identifier
doi:10.1216/RMJ-2017-47-5-1427

Mathematical Reviews number (MathSciNet)
MR3705760

Zentralblatt MATH identifier
06790021

Subjects
Primary: 11D07: The Frobenius problem
Secondary: 11C20: Matrices, determinants [See also 15B36] 13F20: Polynomial rings and ideals; rings of integer-valued polynomials [See also 11C08, 13B25]

Keywords
Frobenius problem polynomials arithmetic of function fields

Citation

Conceição, R.; Gondim, R.; Rodriguez, M. On a Frobenius problem for polynomials. Rocky Mountain J. Math. 47 (2017), no. 5, 1427--1462. doi:10.1216/RMJ-2017-47-5-1427. https://projecteuclid.org/euclid.rmjm/1506045620


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References

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