Basis condition for generalized spline modules

IF 0.6 3区数学 Q3 MATHEMATICS Journal of Algebraic Combinatorics Pub Date : 2024-02-15 DOI:10.1007/s10801-023-01290-y

Seher Fişekci, Samet Sarıoğlan

引用次数: 0

Abstract

A generalized spline on an edge-labeled graph $(G,\alpha )$ is defined as a vertex labeling, such that the difference of labels on adjacent vertices lies in the ideal generated by the edge label. We study generalized splines over greatest common divisor domains and present a determinantal basis condition for generalized spline modules on arbitrary graphs. The main result of the paper answers a conjecture that appeared in several papers.

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广义样条模块的基础条件

边标签图 $(G,\alpha )$ 上的广义样条曲线被定义为一种顶点标签，使得相邻顶点上的标签之差位于边标签所生成的理想中。我们研究了最大公因子域上的广义样条曲线，并提出了任意图上广义样条曲线模块的行列式基础条件。本文的主要结果回答了多篇论文中出现的一个猜想。

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 Algebraic Combinatorics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Algebraic Combinatorics provides a single forum for papers on algebraic combinatorics which, at present, are distributed throughout a number of journals. Within the last decade or so, algebraic combinatorics has evolved into a mature, established and identifiable area of mathematics. Research contributions in the field are increasingly seen to have substantial links with other areas of mathematics. The journal publishes papers in which combinatorics and algebra interact in a significant and interesting fashion. This interaction might occur through the study of combinatorial structures using algebraic methods, or the application of combinatorial methods to algebraic problems.

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