Global Periods Of Words And Partial Words

Let A be a nonempty alphabet.A sequence over A is called a word overA,a sequence over A (?) is called a partial word.The study of the com-binatorial properties of words and partial words is profoundly connectedto numerous fields such as computer science and biology.This paper investigates the global periods of words,partial words withone hole and partial words with two holes.The results are as follows:â‘ Weprovegcd(p₁,p₂,...,p_m)isoneglobalperiodofwordw withglobalperiods p₁,p₂,...,p_m if .This is the main contentof chapter 2.â‘¡We get an appropriate threshold value max(Z(p₁,p₂),Z(gcd(p₁,p₂),p3),...Z(gcd(p₁,p₂,...,p_m ),p_m-1)) which ensures any partial word w∈Em = {w : |H(w)| = 1,p₁,p₂,...,p_m is local periods of w}has a globalperiod gcd(p₁,p₂,...,p_m).This is the main content of chapter 3.â‘¢We get an optimal threshold value max(OPTL(p₁,p₂),OPTG(gcd(p₁,p₂),p3),...,OPTG(gcd(p₁,p₂,...,p_m-1),p_m)) which ensures any partialword w∈E_m = {w : |H(w)| = 2,p₁,p₂,...,p_m is local periods of w} hasa global period gcd(p₁,p₂,...,p_m).We also get an appropriate thresholdvalue when m equals 2.This is the main content of chapter 4.