The Hilton-Milner Theorem For Attenuated Spaces

Let V be an(n+1)-dimensional vector space over a finite field Fq with l,n>0 and W be a fixed l-dimensional subspace of V.Let U be an m-dimensional subspace of V,we say that U is of type(m,k)if dim(U ?W)= k.Denote the set of all subspaces of type(m,k)in V by M(m,k;n+l,n).All the subspaces of type(m,0)in V form the attenuated space,where 0<m<n.In this thesis,we study the properties of the non-trivial intersecting families in the attenuated space.We obtain the cardinality of the maximal non-trivial intersecting family.In particular,when n>m>3,we determine the structure of the maximal non-trivial intersecting families.Hence,we prove the Hilton-Milner theorem for M(m,0;n +l,n)in the attenuated space.