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Uniform probability and natural density of mutually left coprime polynomial matrices over finite fields


Lieb, Julia (2018). Uniform probability and natural density of mutually left coprime polynomial matrices over finite fields. Linear Algebra and its Applications, 539:134-159.

Abstract

We compute the uniform probability that finitely many polynomials over a finite field are pairwise coprime and compare the result with the formula one gets using the natural density as probability measure. It will turn out that the formulas for the two considered probability measures asymptotically coincide but differ in the exact values. Moreover, we calculate the natural density of mutually left coprime polynomial matrices and compare the result with the formula one gets using the uniform probability distribution. The achieved estimations are not as precise as in the scalar case but again we can show asymptotic coincidence.

Abstract

We compute the uniform probability that finitely many polynomials over a finite field are pairwise coprime and compare the result with the formula one gets using the natural density as probability measure. It will turn out that the formulas for the two considered probability measures asymptotically coincide but differ in the exact values. Moreover, we calculate the natural density of mutually left coprime polynomial matrices and compare the result with the formula one gets using the uniform probability distribution. The achieved estimations are not as precise as in the scalar case but again we can show asymptotic coincidence.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:340 Law
610 Medicine & health
510 Mathematics
Scopus Subject Areas:Physical Sciences > Algebra and Number Theory
Physical Sciences > Numerical Analysis
Physical Sciences > Geometry and Topology
Physical Sciences > Discrete Mathematics and Combinatorics
Uncontrolled Keywords:Discrete Mathematics and Combinatorics, Geometry and Topology, Numerical Analysis, Algebra and Number Theory
Language:English
Date:1 February 2018
Deposited On:10 Nov 2021 15:21
Last Modified:26 Apr 2024 01:36
Publisher:Elsevier
ISSN:0024-3795
OA Status:Closed
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1016/j.laa.2017.11.006
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