几乎对称数值半群上的对称性
Symmetries on almost symmetric numerical semigroups
摘要：
几乎对称数值半群的概念是由V.Barucci和R.弗罗伯格我们通过伪弗罗贝纽斯数的对称性来刻画几乎对称数值半群。给出了$H^*$（$M$的对偶）是几乎对称数值半群的一个判别准则.利用这些结果，我们给出了开模数值半群的重数公式。最后，我们证明了如果$H_1$或$H_2$不对称，则$H_1$和$H_2$的胶合不是几乎对称的.
英文摘要：
The notion of almost symmetric numerical semigroup was given by V. Barucci and R. Fröberg. We characterize almost symmetric numerical semigroups by symmetry of pseudo-Frobenius numbers. We give a criterion for $H^*$ (the dual of $M$) to be almost symmetric numerical semigroup. Using these results we give a formula for multiplicity of an opened modular numerical semigroups. Finally, we show that if $H_1$ or $H_2$ is not symmetric, then the gluing of $H_1$ and $H_2$ is not almost symmetric.
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