Numerical semigroups II: Pseudo-symmetric AA-semigroups

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• 作者：Ignacio Garcí ; a-Marco^a ; ^{ignacio.garcia-marco@ens-lyon.fr" class="auth_mail" title="E-mail the corresponding author} ; ^{iggarcia@ull.es" class="auth_mail" title="E-mail the corresponding author} ; Jorge L. Ramí ; rez Alfonsí ; n^b ; ^{jramirez@um2.fr" class="auth_mail" title="E-mail the corresponding author} ; Ø ; ystein J. Rø ; dseth^c ; ^{rodseth@math.uib.no" class="auth_mail" title="E-mail the corresponding author}
• 关键词：05A15 ; 13P10 ; 20M14
• 刊名：Journal of Algebra
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：470
• 期：Complete
• 页码：484-498
• 全文大小：362 K

文摘

In this work we consider the general numerical AA-semigroup, i.e., semigroups consisting of all non-negative integer linear combinations of relatively prime positive integers of the form class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021869316303489&_mathId=si1.gif&_user=111111111&_pii=S0021869316303489&_rdoc=1&_issn=00218693&md5=617183253413683315dfd7faf604b091" title="Click to view the MathML source">a,a+d,a+2d,…,a+kd,cclass="mathContainer hidden">class="mathCode">$a,a+d,a+2d,\dots ,a+kd,c$. We first prove that, in contrast to arbitrary numerical semigroups, there exists an upper bound for the type of AA-semigroups that only depends on the number of generators of the semigroup. We then present two characterizations of pseudo-symmetric AA-semigroups. The first one leads to a polynomial time algorithm to decide whether an AA-semigroup is pseudo-symmetric. The second one gives a method to construct pseudo-symmetric AA-semigroups and provides explicit families of pseudo-symmetric semigroups with arbitrarily large number of generators.