Affine vector space partitions
Preprint
Abstract
An affine vector space partition of $\operatorname{AG}(n,q)$ 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
All Related Versions
This publication has 11 references indexed in Scilit:
- Are hitting formulas hard for resolution?Discrete Applied Mathematics, 2023
- A Generalization of the Cylinder Conjecture for Divisible CodesIEEE Transactions on Information Theory, 2021
- Heden’s bound on the tail of a vector space partitionDiscrete Mathematics, 2018
- On the cylinder conjectureDesigns, Codes and Cryptography, 2018
- Several classes of complete permutation polynomialsFinite Fields and Their Applications, 2014
- On the length of the tail of a vector space partitionDiscrete Mathematics, 2009
- An efficient algorithm for the minimal unsatisfiability problem for a subclass of CNFAnnals of Mathematics and Artificial Intelligence, 1998
- CNF-Satisfiability Test by Counting and Polynomial Average TimeSIAM Journal on Computing, 1989
- Partitions of Finite Abelian GroupsEuropean Journal of Combinatorics, 1986
- Partial spreads in finite projective spaces and partial designsMathematische Zeitschrift, 1975