Abstract

Papa Sissokho (ISU), Partitions of finite vector spaces into subspaces

  • Abstract:

    • Let V be a finite vector space over a finite field. The subspaces W_1, W_2, ..., W_k form a partition of V if

  • (a) each vector u in V belong to some W_i,
  • (b) W_i and W_j only intersect at the 0-vector for i>j.

    • In this talk, we will discuss necessary and sufficient conditions for the existence of a partition of V. In the process, we will define the concept of realizable dimension sequence, which is a sort of vector space analogue of a realizable degree sequence for graphs.

    Last modified: Thurs. Feb. 7, 2007