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">. 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.
