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

Gaydarov, Petar; Delchev, Konstantin

Serdica Journal of Computing (2015)

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

## Access Full Article

top## Abstract

top## How to cite

topGaydarov, 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 -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.