In recent years,more and more researches have been done on the Assouad dimension of sets.The Assouad dimension of some special sets have been studied and calculated by many scholars both at home and abroad.In this paper,we studied a kind of generalized set defined by digit restrictions and calculated its Assouad dimension.The conclusion is as follows:Let Es,(?)is a set defined by digit restrictions and set A.S is a subset of positive integer set N.For any integer m in set N.Set Wm={?1?2
?m:?k?{1,2} if k?S,?k=1if k(?)S,1?k?m}.If word ?=?1?2
?n and v=v1v2
vm,then ?*v=?1
?nv1
vm.Define set(?)and the closed subset A={I?:??W}:(?)I=[0,1]satisfies the following two relations:(1)For any word ? in set Wm,set I? is geometrically similar to set I,that is,there is a similarity mapping f?:R?R such that I?=f?(I)and |I?|=c?|I|.Without loss of generality,set I?=I.If word ?=?1?2
?n,then the compression radio c?=c?1c?2
c?n.(2)For any integer m?0 and any word ? in set Wm,when integer m+1?S,the subsets I?*1 and I?*2 of set I? are disjoint and |I?*1|=ci|I?|,i=1,2;when integer m+1(?)S,we only take the subset I?*1 and |I?*1|=c1|I?|.Let C1 and C2 be the numbers given when the set ES.A is defined,and they are between 0 and 1,let s*be the only real number that satisfies the following equation(?),where(?)is the upper Banach density of set S,then dimAES,A=s*. |