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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.