@article{257bdebfc79e4c5c8ac8604f27869f0a,
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 = "Funding Information: First of all we would like to thank the two anonymous referees for their careful reading and the many useful remarks that improved the presentation of the paper a lot. We thank Esmeralda N{\u a}stase, Artur Riazanov, and Yuriy V. Tarannikov for helpful discussions. Further thanks go to Tom{\'a}{\v s} Peitl and Stefan Szeider for sharing with us the results of the computer search reported in []. Ferdinand Ihringer and Sascha Kurz would like to thank the organizers of the Sixth Irsee Conference on Finite Geometries for their invitation. During that conference the idea of analyzing and introducing avsps slowly evolved, being triggered by some open problems for hitting formulas. This project has received funding from the European Union{\textquoteright}s Horizon 2020 research and innovation programme under grant agreement No 802020-ERC-HARMONIC. Ferdinand Ihringer is supported by a postdoctoral fellowship of the Research Foundation – Flanders (FWO). Publisher Copyright: {\textcopyright} 2023, The Author(s).",
year = "2025",
month = feb,
doi = "10.1007/s10623-023-01263-z",
language = "English",
volume = "93",
pages = "331--357",
journal = "Designs, Codes, and Cryptography",
issn = "0925-1022",
publisher = "Springer",
number = "2",
}