On the maximum field of linearity of linear sets-Reference-Cited by-同舟云学术

On the maximum field of linearity of linear sets

Published:2024-08-13 Issue: Volume: Page:
ISSN:0024-6093
Container-title:Bulletin of the London Mathematical Society
language:en
Short-container-title:Bulletin of London Math Soc

Author:

Csajbók Bence¹^ORCID,Marino Giuseppe²^ORCID,Pepe Valentina³

Affiliation:

1. Dipartimento di Meccanica, Matematica e Management Politecnico di Bari Bari Italy

2. Dipartimento di Matematica e Applicazioni “Renato Caccioppoli” Università degli Studi di Napoli Federico II Napoli Italy

3. Dipartimento di Scienze di Base ed Applicate per l'Ingegneria “Sapienza” Università di Roma Roma Italy

Abstract

AbstractLet denote an ‐dimensional ‐vector space. For an ‐dimensional ‐subspace of , assume that for each nonzero vector . If , then we prove the existence of an integer such that the set of one‐dimensional ‐subspaces generated by nonzero vectors of is the same as the set of one‐dimensional ‐subspaces generated by nonzero vectors of . If we view as a point set of , it means that and determine the same set of directions. We prove a stronger statement when . In terms of linear sets, it means that an ‐linear set of has maximum field of linearity only if it has a point of weight one. We also present some consequences regarding the size of a linear set.

Funder

National Research, Development and Innovation Office

Publisher

Wiley

Link

https://londmathsoc.onlinelibrary.wiley.com/doi/pdf/10.1112/blms.13133

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