Mathematics Commons^™

Intersecting Chains In Finite Vector Spaces, Eva Czabarka

Faculty Publications

We prove an Erdős–Ko–Rado-type theorem for intersecting k-chains of subspaces of a finite vector space. This is the q-generalization of earlier results of Erdős, Seress and Székely for intersecting k-chains of subsets of an underlying set. The proof hinges on the author's proper generalization of the shift technique from extremal set theory to finite vector spaces, which uses a linear map to define the generalized shift operation. The theorem is the following.

For c = 0, 1, consider k-chains of subspaces of an n-dimensional vector space over GF(q), such that the smallest subspace in any chain has dimension at least …