Wilf inequality is preserved under gluing of semigroups

IF 0.5 3区数学 Q3 MATHEMATICS

Journal of Algebra and Its Applications Pub Date : 2024-04-26 DOI:10.1142/s021949882550255x

Srishti Singh, Hema Srinivasan

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引用次数: 0

Abstract

Wilf Conjecture on numerical semigroups is a question posed by Wilf in 1978 and is an inequality connecting the Frobenius number, embedding dimension and the genus of the semigroup. The conjecture is still open in general. We prove that this Wilf inequality is preserved under gluing of numerical semigroups. If the numerical semigroups minimally generated by $A = {a_{1}, \dots, a_{p}}$ and $B = {b_{1}, \dots, b_{q}}$ satisfy the Wilf inequality, then so does their gluing which is minimally generated by $C = k_{1} A ⊔ k_{2} B$ . We discuss the extended Wilf’s Conjecture in higher dimensions for certain affine semigroups and prove an analogous result.

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Wilf 不等式在半群胶合时得到保留

关于数值半群的 Wilf 猜想是 Wilf 于 1978 年提出的一个问题，是连接半群的弗罗贝尼斯数、嵌入维数和属数的不等式。该猜想在一般情况下仍未解决。我们证明，这个 Wilf 不等式在数字半群的胶合作用下得以保留。如果由 A={a1,...ap} 和 B={b1,...bq} 最小生成的数字半群满足 Wilf 不等式，那么由 C=k1A⊔k2B 最小生成的它们的胶合也满足 Wilf 不等式。我们讨论了某些仿射半群在更高维度上的扩展 Wilf 猜想，并证明了一个类似的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Algebra and Its Applications 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

226

审稿时长

4-8 weeks

期刊介绍： The Journal of Algebra and Its Applications will publish papers both on theoretical and on applied aspects of Algebra. There is special interest in papers that point out innovative links between areas of Algebra and fields of application. As the field of Algebra continues to experience tremendous growth and diversification, we intend to provide the mathematical community with a central source for information on both the theoretical and the applied aspects of the discipline. While the journal will be primarily devoted to the publication of original research, extraordinary expository articles that encourage communication between algebraists and experts on areas of application as well as those presenting the state of the art on a given algebraic sub-discipline will be considered.