Proportionally Modular Diophantine Inequalities and Full Semigroups

  title={Proportionally Modular Diophantine Inequalities and Full Semigroups},
  author={Jos{\'e} Carlos Rosales and J. M. Urbano-Blanco},
A proportionally modular numerical semigroup is the set of nonnegative integer solutions to a Diophantine inequality of the type axmod b ≤ cx . We give a new presentation for these semigroups and we relate them with a type of affine full semigroups. Next, we describe explicitly the minimal generating system for the affine full semigroups we are considering. As a consequence, we obtain generating systems for proportionally modular numerical semigroups and we exhibit several families of these… CONTINUE READING

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