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Paper   IPM / M / 15189
School of Mathematics
  Title:   Homogeneous numerical semigroups
  Author(s):  Raheleh Jafari (Joint with S. Z. Armengou)
  Status:   Published
  Journal: Semigroup Forum
  Vol.:  97
  Year:  2018
  Pages:   278-306
  Supported by:  IPM
  Abstract:
We introduce the concept of homogeneous numerical semigrou ps and show that all homogeneous numerical semigroups with Cohen- Macaulay tangent cones are of homogeneous type. In embedding dimension three, we cl assify all numerical semigroups of homogeneous type into numerical semigroups w ith complete intersec- tion tangent cones and the homogeneous ones which are not sym metric with Cohen- Macaulay tangent cones. We also study the behavior of the hom ogeneous property by gluing and shiftings to construct large families of homogen eous numerical semigroups with Cohen-Macaulay tangent cones. In particular we show th at these properties fulfill asymptotically in the shifting classes. Several exp licit examples are provided along the paper to illustrate the property.

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