非对称数值半群中的间隙
Gaps in Nonsymmetric Numerical Semigroups
摘要：
在由最小正整数集{d_1，.，d_m}。h-能隙只对非对称半群有特殊的性质，而g-能隙对对称和非对称半群都有。我们导出了相应的间隙集的生成函数Delta_H（{ \bf d}^m）和Delta_G（{ \bf d}^m），并证明了关于h-间隙的最小值和最大值的几个命题.对三种特殊的非对称半群：具有最大嵌入维数的半群，具有最大和几乎最大长度的半群，以及伪对称半群，给出了这两类间隙的详细描述。
英文摘要：
There exist two different sorts of gaps in the nonsymmetric numerical additive semigroups finitely generated by a minimal set of positive integers {d_1,...,d_m}. The h-gaps are specific only for the nonsymmetric semigroups while the g-gaps are possessed by both, symmetric and nonsymmetric semigroups. We derive the generating functions for the corresponding sets of gaps, Delta_H({\bf d}^m) and Delta_G({\bf d}^m), and prove several statements on the minimal and maximal values of the h-gaps. Detailed description of both sorts of gaps is given for three special kinds of nonsymmetric semigroups: semigroups with maximal embedding dimension, semigroups of maximal and almost maximal length, and pseudo--symmetric semigroups.
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