The geometric field of linearity of linear sets

Jena, Dibyayoti; Voorde, Geertrui Van de

doi:10.48550/arxiv.2109.12749

Search citation statements

Order By: Relevance

Paper Sections

Select...

Linear Sets1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2022

Publication Types

Select...

Other1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Regarding the linearity of a linear set, more attention has to be paid as pointed out by Jena and Van de Voorde in [12]. Definition 2.1.…”

Section: Linear Setsmentioning

confidence: 99%

Classifications and constructions of minimum size linear sets

Napolitano¹,

Polverino²,

Santonastaso³

et al. 2022

Preprint

View full text Add to dashboard Cite

This paper aims to study linear sets of minimum size in the projective line, that is F q -linear sets of rank k in PG(1, q n ) admitting one point of weight one and having size q k−1 + 1. Examples of these linear sets have been found by Lunardon and the second author ( 2000) and, more recently, by Jena and Van de Voorde (2021). However, classification results for minimum size linear sets are known only for k ≤ 5. In this paper we provide classification results for those L U admitting two points with complementary weights. We construct new examples and also study the related ΓL(2, q n )-equivalence issue. These results solve an open problem posed by Jena and Van de Voorde. The main tool relies on two results by Bachoc, Serra and Zémor (2017 and 2018) on the linear analogues of Kneser's and Vosper's theorems. We then conclude the paper pointing out a connection between critical pairs and linear sets, obtaining also some classification results for critical pairs.

show abstract

“…Regarding the linearity of a linear set, more attention has to be paid as pointed out by Jena and Van de Voorde in [12]. Definition 2.1.…”

Section: Linear Setsmentioning

confidence: 99%