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.