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, Δ H (d m ) and Δ g (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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机译：由最小正整数{d 1 ，...，d m }的有限集合有限生成的非对称数值加法半群中存在两种不同类型的间隙。 h间隙仅特定于非对称半群，而g间隙由对称半群和非对称半群同时拥有。我们推导了相应的间隙集Δ H （d m ）和Δ g （d m ），并证明有关h间隙的最小值和最大值的几种说法。针对三种特殊类型的非对称半群对两种间隙进行了详细描述：具有最大嵌入维数的半群，最大和几乎最大长度的半群以及伪对称半群。
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