Betti numbers for numerical semigroup rings

@article{Stamate2016BettiNF,
  title={Betti numbers for numerical semigroup rings},
  author={Dumitru I. Stamate},
  journal={arXiv: Commutative Algebra},
  year={2016}
}
We survey results related to the magnitude of the Betti numbers of numerical semigroup rings and of their tangent cones. 
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On the Betti numbers of the tangent cones for Gorenstein monomial curves
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    TURKISH JOURNAL OF MATHEMATICS
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Let S denote the numerical semigroup generated by the positive integers n1 < n2 < . . . < nd with gcd(n1, . . . , nd) = 1. Consider the polynomial rings R = k[x1, . . . , xd] and k[t] over the field
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