Affine vector space partitions

John Bamberg; Yuval Filmus; Ferdinand Ihringer; Sascha Kurz

doi:10.1007/s10623-023-01263-z

Affine vector space partitions

John Bamberg, Yuval Filmus, Ferdinand Ihringer, Sascha Kurz

Computer Science

Technion - Israel Institute of Technology

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

Abstract

An affine vector space partition of AG(n,q) is a set of proper affine subspaces that partitions the set of points. Here we determine minimum sizes and enumerate equivalence classes of affine vector space partitions for small parameters. We also give parametric constructions for arbitrary field sizes.

Original language	English
Journal	Designs, Codes, and Cryptography
DOIs	https://doi.org/10.1007/s10623-023-01263-z
State	Accepted/In press - 2023

Keywords

Fano plane
Finite geometry
Hitting formulas
Klein quadric
Spreads
Vector space partitions

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science Applications
Discrete Mathematics and Combinatorics
Applied Mathematics

Access to Document

10.1007/s10623-023-01263-z

Cite this

@article{fe97e4c673974c538342ecfbbcc11c79,

title = "Affine vector space partitions",

abstract = "An affine vector space partition of AG(n,q) is a set of proper affine subspaces that partitions the set of points. Here we determine minimum sizes and enumerate equivalence classes of affine vector space partitions for small parameters. We also give parametric constructions for arbitrary field sizes.",

keywords = "Fano plane, Finite geometry, Hitting formulas, Klein quadric, Spreads, Vector space partitions",

author = "John Bamberg and Yuval Filmus and Ferdinand Ihringer and Sascha Kurz",

note = "Publisher Copyright: {\textcopyright} 2023, The Author(s).",

year = "2023",

doi = "10.1007/s10623-023-01263-z",

language = "الإنجليزيّة",

journal = "Designs, Codes, and Cryptography",

issn = "0925-1022",

publisher = "Springer Netherlands",

}

TY - JOUR

T1 - Affine vector space partitions

AU - Bamberg, John

AU - Filmus, Yuval

AU - Ihringer, Ferdinand

AU - Kurz, Sascha

PY - 2023

Y1 - 2023

N2 - An affine vector space partition of AG(n,q) is a set of proper affine subspaces that partitions the set of points. Here we determine minimum sizes and enumerate equivalence classes of affine vector space partitions for small parameters. We also give parametric constructions for arbitrary field sizes.

AB - An affine vector space partition of AG(n,q) is a set of proper affine subspaces that partitions the set of points. Here we determine minimum sizes and enumerate equivalence classes of affine vector space partitions for small parameters. We also give parametric constructions for arbitrary field sizes.

KW - Fano plane

KW - Finite geometry

KW - Hitting formulas

KW - Klein quadric

KW - Spreads

KW - Vector space partitions

UR - http://www.scopus.com/inward/record.url?scp=85162930698&partnerID=8YFLogxK

U2 - 10.1007/s10623-023-01263-z

DO - 10.1007/s10623-023-01263-z

M3 - مقالة

SN - 0925-1022

JO - Designs, Codes, and Cryptography

JF - Designs, Codes, and Cryptography

ER -

Affine vector space partitions

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this