# Combinatorial Computations on an Extension of a Problem by Pál Turán

• Volume: 9, Issue: 3-4, page 257-268
• ISSN: 1312-6555

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## Abstract

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Turan’s problem asks what is the maximal distance from a polynomial to the set of all irreducible polynomials over Z. It turns out it is sufficient to consider the problem in the setting of F2. Even though it is conjectured that there exists an absolute constant C such that the distance L(f - g) <= C, the problem remains open. Thus it attracts different approaches, one of which belongs to Lee, Ruskey and Williams, who study what the probability is for a set of polynomials ‘resembling’ the irreducibles to satisfy this conjecture. In the following article we strive to provide more precision and detail to their method, and propose a table with better numeric results. ACM Computing Classification System (1998): H.1.1. *This author is partially supported by the High School Students Institute of Mathematics and Informatics.

## How to cite

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Gaydarov, Petar, and Delchev, Konstantin. "Combinatorial Computations on an Extension of a Problem by Pál Turán." Serdica Journal of Computing 9.3-4 (2015): 257-268. <http://eudml.org/doc/289530>.

@article{Gaydarov2015,
abstract = {Turan’s problem asks what is the maximal distance from a polynomial to the set of all irreducible polynomials over Z. It turns out it is sufficient to consider the problem in the setting of F2. Even though it is conjectured that there exists an absolute constant C such that the distance L(f - g) <= C, the problem remains open. Thus it attracts different approaches, one of which belongs to Lee, Ruskey and Williams, who study what the probability is for a set of polynomials ‘resembling’ the irreducibles to satisfy this conjecture. In the following article we strive to provide more precision and detail to their method, and propose a table with better numeric results. ACM Computing Classification System (1998): H.1.1. *This author is partially supported by the High School Students Institute of Mathematics and Informatics.},
author = {Gaydarov, Petar, Delchev, Konstantin},
journal = {Serdica Journal of Computing},
keywords = {Irreducible Polynomials; Distance Sets; Finite Fields},
language = {eng},
number = {3-4},
pages = {257-268},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Combinatorial Computations on an Extension of a Problem by Pál Turán},
url = {http://eudml.org/doc/289530},
volume = {9},
year = {2015},
}

TY - JOUR
AU - Gaydarov, Petar
AU - Delchev, Konstantin
TI - Combinatorial Computations on an Extension of a Problem by Pál Turán
JO - Serdica Journal of Computing
PY - 2015
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 9
IS - 3-4
SP - 257
EP - 268
AB - Turan’s problem asks what is the maximal distance from a polynomial to the set of all irreducible polynomials over Z. It turns out it is sufficient to consider the problem in the setting of F2. Even though it is conjectured that there exists an absolute constant C such that the distance L(f - g) <= C, the problem remains open. Thus it attracts different approaches, one of which belongs to Lee, Ruskey and Williams, who study what the probability is for a set of polynomials ‘resembling’ the irreducibles to satisfy this conjecture. In the following article we strive to provide more precision and detail to their method, and propose a table with better numeric results. ACM Computing Classification System (1998): H.1.1. *This author is partially supported by the High School Students Institute of Mathematics and Informatics.
LA - eng
KW - Irreducible Polynomials; Distance Sets; Finite Fields
UR - http://eudml.org/doc/289530
ER -

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