Constructing numerical semigroups of a given genus
Constructing numerical semigroups of a given genus
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构造给定属的数值半群
DOI：
10.1007/s00233-009-9190-9
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发表时间：
2009
期刊：
影响因子：
0.7
通讯作者：
Yufei Zhao
中科院分区：
文献类型：
--
作者：
Yufei Zhao
令 ng 表示属 g 的数值半群的数量。 Bras-Amorós 推测 ng 具有某些类似斐波那契的性质。几乎所有先前证明这个猜想的尝试都是基于分析半群树。我们提供了一种新的、更简单的方法来计算给定属的数值半群。我们的方法给出了数值半群族的直接构造，而不参考生成器或半群树。特别是，我们给出了 ng 的改进渐近下界。
Let ng denote the number of numerical semigroups of genus g. Bras-Amorós conjectured that ng possesses certain Fibonacci-like properties. Almost all previous attempts at proving this conjecture were based on analyzing the semigroup tree. We offer a new, simpler approach to counting numerical semigroups of a given genus. Our method gives direct constructions of families of numerical semigroups, without referring to the generators or the semigroup tree. In particular, we give an improved asymptotic lower bound for ng.