Heden's bound on the tail of a vector space partition

Titelangaben

Kurz, Sascha:
Heden's bound on the tail of a vector space partition.
Bayreuth , 2018 . - 5 S.

Volltext

	Format: PDF Name: tail_heden.pdf Version: Veröffentlichte Version Verfügbar mit der Lizenz Creative Commons BY 4.0: Namensnennung
	Download (246kB)

Abstract

A vector space partition of GF(q)^v is a collection of subspaces such that every non-zero vector is contained in a unique element. We improve a lower bound of Heden, in a subcase, on the number of elements of the smallest occurring dimension in a vector space partition. To this end, we introduce the notion of q^r-divisible sets of k-subspaces in GF(q)^v. By geometric arguments we obtain non-existence results for these objects, which then imply the improved result of Heden.