Research Of The Erd?s-Ko-Rado Theorem Based On Symplectic Spaces Over Finite Fields

The Erd?s-Ko-Rado?EKR?theorem,the earliest result in the researching families of a finite set,deals with the intersecting property of set.It is also one of the classical conclusions in extreme set theory.Therefore,the EKR theorem has great research value and development prospects.In the last decades,lots of scholars have conducted various forms of promotion and got many forms of EKR theorem.In this thesis,efficiently combine the geometry of classical groups over finite fields to study the EKR theorem of the symplectic spaces over finite fields.The Erd?s-Ko-Rado theorem of totally isotropic subspaces and non-isotropic subspaces are studied respectively.1.The Erd?s-Ko-Rado theorem of totally isotropic subspaces of type?m,0?based on symplectic spaces over finite fields.Using concept of totally isotropic subspaces and the anzahl theorems in symplectic spaces,adding special vectors which meet certain conditions to the subspaces of type?r,0?to get a new space which is concluded in the subspaces of type?m,0?.Combining the methods of relating the Erd?s-Ko-Rado theorem to confirm supremum of r-intersecting of the totally isotropic subspaces of type?m,0?in the symplectic spaces over the finite fields by making use of the result of studying montonoicity of functions.2.The Erd?s-Ko-Rado theorem of non-isotropic subspaces of type?2m,m?based on symplectic spaces over the finite fields.Making use of concept of non-isotropic subspaces of type?2m,m?and the anzahl theorem in symplectic spaces and to compare with the number of non-isotropic subspaces of type?2m,m?containing a given subspaces of type?m₁,s₁?and type?m₁,s₁+1?and to confirm the type of new spaces after adding vectors to sub spaces of type?r,s?.Combining the methods of relating the Erd?s-Ko-Rado theorem to confirm supremum of r-intersecting of the non-isotropic subspaces of type?2m,m?based on symplectic spaces over finite fields by adding vectors and studying montonoicity of functions.