Polar Coordinates View on KM-Arcs

Kanat Abdukhalikov; Duy Ho

doi:10.1007/s00373-021-02366-x

Polar Coordinates View on KM-Arcs

Kanat Abdukhalikov, Duy Ho

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We study presentations of KM-arcs in polar coordinates. New characterizations on the point set of KM-arcs are obtained in terms of power sums and bilinear forms. Therefore, we provide purely algebraic criteria for the existence of KM-arcs. We also describe some constructions of KM-arcs which include known examples and describe their automorphism groups in this presentation.

Original language	English
Pages (from-to)	1467-1490
Number of pages	24
Journal	Graphs and Combinatorics
Volume	37
Issue number	5
DOIs	https://doi.org/10.1007/s00373-021-02366-x
Publication status	Published - Sept 2021

Keywords

Arcs
Hyperovals
Ovals
Power sums
Vandermonde sets

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1007/s00373-021-02366-x

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title = "Polar Coordinates View on KM-Arcs",

abstract = "We study presentations of KM-arcs in polar coordinates. New characterizations on the point set of KM-arcs are obtained in terms of power sums and bilinear forms. Therefore, we provide purely algebraic criteria for the existence of KM-arcs. We also describe some constructions of KM-arcs which include known examples and describe their automorphism groups in this presentation.",

keywords = "Arcs, Hyperovals, Ovals, Power sums, Vandermonde sets",

author = "Kanat Abdukhalikov and Duy Ho",

note = "Funding Information: This research was supported by UAEU Grant 31S366. Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer Japan KK, part of Springer Nature.",

year = "2021",

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AU - Abdukhalikov, Kanat

AU - Ho, Duy

PY - 2021/9

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N2 - We study presentations of KM-arcs in polar coordinates. New characterizations on the point set of KM-arcs are obtained in terms of power sums and bilinear forms. Therefore, we provide purely algebraic criteria for the existence of KM-arcs. We also describe some constructions of KM-arcs which include known examples and describe their automorphism groups in this presentation.

AB - We study presentations of KM-arcs in polar coordinates. New characterizations on the point set of KM-arcs are obtained in terms of power sums and bilinear forms. Therefore, we provide purely algebraic criteria for the existence of KM-arcs. We also describe some constructions of KM-arcs which include known examples and describe their automorphism groups in this presentation.

KW - Arcs

KW - Hyperovals

KW - Ovals

KW - Power sums

KW - Vandermonde sets

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JO - Graphs and Combinatorics

JF - Graphs and Combinatorics

IS - 5

ER -

Polar Coordinates View on KM-Arcs

Abstract

Keywords

ASJC Scopus subject areas

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