Numerical semigroups with many gaps of the same parity |
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| Authors: | J. C. Rosales P. Vasco |
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| Affiliation: | (1) Departamento de álgebra, Universidad de Granada, 18071 Granada, Spain;(2) Departamento de Matemática, Universidade de Trás-os-Montes e Alto Douro, 5001-801 Vila Real, Portugal |
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| Abstract: | Let g e (S) (respectively, g o (S)) be the number of even (respectively, odd) gaps of a numerical semigroup S. In this work we study and characterize the numerical semigroups S that verify 2|g e (S)−g o (S)|+1∈S. As a consequence we will see that every numerical semigroup can be represented by means of a numerical semigroup with maximal embedding dimension with all its minimal generators odd. The first author is supported by the project MTM2007-62346 and FEDER funds. The authors want to thank P.A. García-Sánchez and the referee for their comments and suggestions. |
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| Keywords: | Numerical semigroup Gaps Frobenius number Singularity degree Maximal embedding dimension |
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