Affine vector space partitions

2024/07/02 by Bamberg, John, Filmus, Yuval, Ihringer, Ferdinand +1
#004 #510 #Fano plane #Klein quadric #finite geometry #hitting formulas #spreads #vector space partitions

paper · doi:10.15495/epub_ubt_00007765

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.

Related

• A note on Tight Irreducible Affine Spreads
• Vector space partitions of GF(2)⁸
• Avoiding intersections of given size in finite affine spaces AG(n,2)
• A survey of the different types of vector space partitions
• Some necessary conditions for vector space partitions