Some criteria for type sequences of numerical semigroups

ABSTRACT This study consists of five chapters. In the first chapter, general informations on the Numerical Semigroups and their type sequences are given. The second chapter consists of the different methods used to find type sequences of numerical semigroups. In the third chapter, numerical semigroups beginning with 3 and 4, referred to also as " Weierstrass semigroups " are discussed. The fourth chapter is the first principal part of our study. Namely, let S be a numerical semigroup, t e N and t > 3. The sequence {^2} is the type of sequence of following numerical semigroup with n(S)=2: S={o, tx +1,?!+ t2 + 2, ->...}, where tx =2t + \ and t2 =t. The sequence {tx,t2,t3 } is the type of sequence of following numerical semigroup with n(S)=3: S = { 0, t{ +1, tx +t2 +2,h +h +t3 +3,->...} where tx =4^+1, t2 =2/+l and /3 =t The sequence {h,t2,ti,tA } is the type of sequence of following numerical semigroup with n ( 5" ) = 4 : S = { 0, tx +X tx +t2 +2,tx +t2 +t3 +3,tx +t2 +t3 +t4 +4, ^... } where tx =St+l,t2 =4^+1, t3 =2t+l and t4 =t. The last chapter is the second principal part of our study. Here, the necessary criteria for a numerical semigroup to be ARF or symmetric semigroup are found. m