{"title":"Rigid frameworks with dilation constraints","authors":"Sean Dewar , Anthony Nixon , Andrew Sainsbury","doi":"10.1016/j.disc.2024.114304","DOIUrl":null,"url":null,"abstract":"<div><div>We consider the rigidity and global rigidity of bar-joint frameworks in Euclidean <em>d</em>-space under additional dilation constraints in specified coordinate directions. In this setting we obtain a complete characterisation of generic rigidity. We then consider generic global rigidity. In particular, we provide an algebraic sufficient condition and a weak necessary condition. We also construct a large family of globally rigid frameworks and conjecture a combinatorial characterisation when most coordinate directions have dilation constraints.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 2","pages":"Article 114304"},"PeriodicalIF":0.7000,"publicationDate":"2024-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0012365X24004357","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
We consider the rigidity and global rigidity of bar-joint frameworks in Euclidean d-space under additional dilation constraints in specified coordinate directions. In this setting we obtain a complete characterisation of generic rigidity. We then consider generic global rigidity. In particular, we provide an algebraic sufficient condition and a weak necessary condition. We also construct a large family of globally rigid frameworks and conjecture a combinatorial characterisation when most coordinate directions have dilation constraints.
期刊介绍：
Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory.
Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.
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