The Erd?s-Ko-Rado Theorem For Finite Affine Symplectic Space

The Erd?s-Ko-Rado theorem is an important theorem of extreme value combination theory.There are corresponding to the Erd?s-Ko-Rado theorem for vector space,semi-lattices,bilinear forms space.In this thesis we will discuss the Erd?s-Ko-Rado theorem for finite affine symplectic space.Let F_q^?2v?denote the 2v-dimensional row vector space over the finite filed F,and letbe a subspace of type?m,r?in the symplectic space F_q^?2v?.A coset P+x of P is called an?m,r?-flat,where x?F_q^?2v?.The point set F_q^?2v?with all the flats and the incidence relation among them is said to be the 2v-dimensional affine symplectic space.Let X_k be the set of all?k,0?-flats of affine symplectic space.A nonempty family F???X_k is called-intersecting if dim?F₁?F₂??t for all F₁,F₂?F.In this paper,we determine the maximum size of 0- intersecting and 1- intersecting family in the subset X_k and describe the structures of F which reach these upper bounds,which is called the Erd?s-Ko-Rado theorem of affine finite symplectic space.