一个具有Markov性的入圈问题

A Problem on Markov Properties of Circular Interpolation

研究序列{Xn},{Xn}满足Xn=Yn(mod 2),其中Yn∈Z+,Y0≥2,Yn+1=Yn+[Yn/2],证明了{Xn}为一独立随机变量序列,并且是一时间齐次Markov链.最后,利用该Markov链{Xn}的性质,证明了入圈问题经过有限次插点,Cm的任意一边上都至少插入一个新点.

In this paper, a sequence{Xn} is considered. It satisfies the equationXn = Yn（mod 2） in which Yn∈Z＋, Y0≥2, Yn＋1 = Yn ＋ [Yn/2]. It is proved that the sequence{Xn} is an independent random variables sequence and a time homogeneous Markov chain. Based on the properties of the Markov chain{X n} , it is demonstrated that any edge of the initial circle C m is interpolated at least one new node after finite steps of circular interpolation.