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SYSTEMS OF INEQUALITIES AND NUMERICAL SEMIGROUPS

  • J. C. ROSALES (a1), P. A. GARCÍA-SÁNCHEZ (a1), J. I. GARCÍA-GARCÍA (a1) and M. B. BRANCO (a2)

Abstract

A one-to-one correspondence is described between the set ${\cal J}(m)$ of numerical semigroups with multiplicity $m$ and the set of non-negative integer solutions of a system of linear Diophantine inequalities. This correspondence infers in ${\cal J}(m)$ a semigroup structure and the resulting semigroup is isomorphic to a subsemigroup of ${\bb N}^{m-1}$ . Finally, this result is particularized to the symmetric case.

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This paper was supported by the project BFM2000-1469.

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