Ramsey数与约束共存性

On Ramsey numbers and restriction coexistence

提出约束共存性概念,并证明约束共存极小状态的存在性,以及它与Ramsey定理所描述的Ramsey现象的等效性.用数量表示这种等效性。

The existence of minimal states under the restriction coexistence is verified.From this it is got another equivalence definition on Ramsey numbers,that is r(p1-1,…,pk-1,pk)=R(p1,…,pk)where pk=max1≤i≤k{pi},pi≥2 all are integers.Some basic relations obtained,for examples R(p,q)≥R(p-1,q+1),3≤o≤q, r(p,p)=r(p-1,p+1)(=R(p,p+1),p≥2),when R(p,q)≤R(u,v),2≤p≤q;p<u≤v,then R(p,q+1)-R(p,q)≤R(u,v+1)-R(u,v)and so on,can improve the present lower and upper bounds on Ramsey numbers within a wide range.