Abstract
A simple way of computing the Apéry set of a numerical semigroup (or monoid) with respect to a generator, using Groebner bases, is presented, together with a generalization for affine semigroups. This computation allows us to calculate the type set and, henceforth, to check the Gorenstein condition which characterizes the symmetric numerical subgroups.
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Notes
Note that, if one needs a square matrix, as some computer algebra packages do, one can always add a numb variable or erase a row between the \(3\)rd and the \((k+1)\)-th.
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Acknowledgments
The authors wish to thank P. García-Sánchez, for pointing us the example which eventually led to Theorem 15, to J.L. Ramírez-Alfonsín and M. D’Anna for their help and advice and also to S. Robbins for his enlightening conversations during his stay in Seville in December 2013.
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Communicated by Fernando Torres.
First and third authors were partially supported by the grant FQM–218 and P12–FQM–2696 (FEDER and FSE). The second author is partially supported by the project MTM2012-36917-C03-01, National Plan I+D+I and by Junta de Extremadura (FEDER funds).
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Márquez-Campos, G., Ojeda, I. & Tornero, J.M. On the computation of the Apéry set of numerical monoids and affine semigroups. Semigroup Forum 91, 139–158 (2015). https://doi.org/10.1007/s00233-014-9631-y
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DOI: https://doi.org/10.1007/s00233-014-9631-y