Systems of Inequalities and Numerical Semigroups | Zendy

Rosales J. C. | Zendy; García-Sánchez P. A. | Zendy; García-García J. I. | Zendy; Branco M. B. | Zendy

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Systems of Inequalities and Numerical Semigroups

Author(s) -

Rosales J. C.,

García-Sánchez P. A.,

García-García J. I.,

Branco M. B.

Publication year - 2002

Publication title -

journal of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.441

H-Index - 62

eISSN - 1469-7750

pISSN - 0024-6107

DOI - 10.1112/s0024610701003052

Subject(s) - numerical semigroup , semigroup , mathematics , multiplicity (mathematics) , diophantine equation , inequality , set (abstract data type) , integer (computer science) , pure mathematics , discrete mathematics , mathematical analysis , computer science , programming language

A one‐to‐one correspondence is described between the set S( 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 S( m ) a semigroup structure and the resulting semigroup is isomorphic to a subsemigroup of N m −1 . Finally, this result is particularized to the symmetric case.

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