On Partitions of Finite vector Spaces

Details On Partitions of Finite vector Spaces On Partitions of Finite vector Spaces

2009-02-18

arxiv.org/abs/0902.3075v1

Mathematics

Combinatorics

14 pages

Scientific paper

In this note, we give a new necessary condition for the existence of non-trivial partitions of a finite vector space. Precisely, we prove that, if V is a finite vector space over a field of order q, then the number of the subspaces of minimum dimension t of a non-trivial partition of V is greater than or equal to q+t. Moreover, we give some extensions of a well known Beutelspacher-Heden's result on existence of T-partitions.

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