大小型的数值半群

IF 0.5 2区数学 Q3 MATHEMATICS

International Journal of Algebra and Computation Pub Date : 2020-08-18 DOI:10.1142/S0218196721500417

Deepesh Singhal

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引用次数: 1

摘要

数值半群是具有有限补的自然数的子半群。数值半群的一些关键性质是它的Frobenius数[公式:见文]，属[公式:见文]和类型[公式:见文]。已知对于任何数值半群[公式:见正文]。具有[公式:见文本]的数值半群称为几乎对称，我们引入一个新的性质来描述它们。我们给出了数值半群的显式刻画[公式:见原文]。我们证明了对于一个固定的[公式:见文]，具有Frobenius数[公式:见文]和类型[公式:见文]的数值半群的数量最终是恒定的[公式:见文]。具有属[公式:见文]和类型[公式:见文]的数值半群的数目最终对于大[公式:见文]也是恒定的。

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Numerical semigroups of small and large type

A numerical semigroup is a sub-semigroup of the natural numbers that has a finite complement. Some of the key properties of a numerical semigroup are its Frobenius number [Formula: see text], genus [Formula: see text] and type [Formula: see text]. It is known that for any numerical semigroup [Formula: see text]. Numerical semigroups with [Formula: see text] are called almost symmetric, we introduce a new property that characterizes them. We give an explicit characterization of numerical semigroups with [Formula: see text]. We show that for a fixed [Formula: see text] the number of numerical semigroups with Frobenius number [Formula: see text] and type [Formula: see text] is eventually constant for large [Formula: see text]. The number of numerical semigroups with genus [Formula: see text] and type [Formula: see text] is also eventually constant for large [Formula: see text].

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来源期刊

International Journal of Algebra and Computation 数学-数学

CiteScore

1.20

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： The International Journal of Algebra and Computation publishes high quality original research papers in combinatorial, algorithmic and computational aspects of algebra (including combinatorial and geometric group theory and semigroup theory, algorithmic aspects of universal algebra, computational and algorithmic commutative algebra, probabilistic models related to algebraic structures, random algebraic structures), and gives a preference to papers in the areas of mathematics represented by the editorial board.