On the cylinder conjecture

Sam Mattheus; Jan De Beule; Jeroen Demeyer; Peter Sziklai

doi:10.1007/s10623-018-0571-5

On the cylinder conjecture

Sam Mattheus, Jan De Beule, Jeroen Demeyer, Peter Sziklai

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3 Citaten (Scopus)

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In this paper, we associate a weight function with a set of points satisfying the conditions of the cylinder conjecture. Then we derive properties of this weight function using the Rédei polynomial of the point set. Using additional assumptions on the number of non-determined directions, together with an exhaustive computer search for weight functions satisfying particular properties, we prove a relaxed version of the cylinder conjecture for p≤ 13. This result also slightly refines a result of Sziklai on point sets in AG (3 , p).

Originele taal-2	English
Pagina's (van-tot)	879-893
Aantal pagina's	15
Tijdschrift	Designs, Codes and Cryptography
Volume	87
Nummer van het tijdschrift	4
DOI's	https://doi.org/10.1007/s10623-018-0571-5
Status	Published - 15 apr 2019

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title = "On the cylinder conjecture",

abstract = "In this paper, we associate a weight function with a set of points satisfying the conditions of the cylinder conjecture. Then we derive properties of this weight function using the R{\'e}dei polynomial of the point set. Using additional assumptions on the number of non-determined directions, together with an exhaustive computer search for weight functions satisfying particular properties, we prove a relaxed version of the cylinder conjecture for p≤ 13. This result also slightly refines a result of Sziklai on point sets in AG (3 , p).",

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AU - De Beule, Jan

AU - Demeyer, Jeroen

AU - Sziklai, Peter

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AB - In this paper, we associate a weight function with a set of points satisfying the conditions of the cylinder conjecture. Then we derive properties of this weight function using the Rédei polynomial of the point set. Using additional assumptions on the number of non-determined directions, together with an exhaustive computer search for weight functions satisfying particular properties, we prove a relaxed version of the cylinder conjecture for p≤ 13. This result also slightly refines a result of Sziklai on point sets in AG (3 , p).

KW - Affine space

KW - Cylinder conjecture

KW - Polynomial method

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ER -

On the cylinder conjecture

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