{"title":"Basis condition for generalized spline modules","authors":"Seher Fişekci, Samet Sarıoğlan","doi":"10.1007/s10801-023-01290-y","DOIUrl":null,"url":null,"abstract":"<p>A generalized spline on an edge-labeled graph <span>\\((G,\\alpha )\\)</span> 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.\n</p>","PeriodicalId":14926,"journal":{"name":"Journal of Algebraic Combinatorics","volume":"26 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebraic Combinatorics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10801-023-01290-y","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
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.
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.