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Computing denumerants in numerical 3-semigroups

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10.2989/16073606.2017.1419998
 
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Aguiló Gost, Francisco de Asis L.Més informacióMés informacióMés informació
Llena, David
Document typeArticle
Defense date2018
Rights accessOpen Access
All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder
Abstract
As far as we know, usual computer algebra packages can not compute denumerants for almost medium (about a hundred digits) or almost medium-large (about a thousand digits) input data in a reasonably time cost on an ordinary computer. Implemented algorithms can manage numerical n-semigroups for small input data. Basically, the denumerant of a non-negative element s ¿ N is the number of non-negative integer solutions of certain linear non-negative Diophantine equation which constant term is equal to s. Here we are interested in denumerants of numerical 3-semigroups which have almost medium input data. A new algorithm for computing denumerants is given for this task. It can manage almost medium input data in the worst case and medium-large or even large input data in some cases.
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This is an Accepted Manuscript of an article published by Taylor & Francis Group in Quaestiones mathematicae on 2018, available online at: http://www.tandfonline.com/10.2989/16073606.2017.1419998.
CitationAguilo, F., Llena, D. Computing denumerants in numerical 3-semigroups. "Quaestiones mathematicae", 2018, vol. 41, núm. 8, p. 1-32. 
URIhttp://hdl.handle.net/2117/125599
DOI10.2989/16073606.2017.1419998
ISSN1607-3606
Publisher versionhttps://www.tandfonline.com/doi/pdf/10.2989/16073606.2017.1419998
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