{"title":"体积刚性和代数移动","authors":"","doi":"10.1016/j.jctb.2024.09.002","DOIUrl":null,"url":null,"abstract":"<div><div>We study the generic volume-rigidity of <span><math><mo>(</mo><mi>d</mi><mo>−</mo><mn>1</mn><mo>)</mo></math></span>-dimensional simplicial complexes in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi><mo>−</mo><mn>1</mn></mrow></msup></math></span>, and show that the volume-rigidity of a complex can be identified in terms of its exterior shifting. In addition, we establish the volume-rigidity of triangulations of several 2-dimensional surfaces and prove that, in all dimensions >1, volume-rigidity is <em>not</em> characterized by a corresponding hypergraph sparsity property.</div></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Volume rigidity and algebraic shifting\",\"authors\":\"\",\"doi\":\"10.1016/j.jctb.2024.09.002\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We study the generic volume-rigidity of <span><math><mo>(</mo><mi>d</mi><mo>−</mo><mn>1</mn><mo>)</mo></math></span>-dimensional simplicial complexes in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi><mo>−</mo><mn>1</mn></mrow></msup></math></span>, and show that the volume-rigidity of a complex can be identified in terms of its exterior shifting. In addition, we establish the volume-rigidity of triangulations of several 2-dimensional surfaces and prove that, in all dimensions >1, volume-rigidity is <em>not</em> characterized by a corresponding hypergraph sparsity property.</div></div>\",\"PeriodicalId\":54865,\"journal\":{\"name\":\"Journal of Combinatorial Theory Series B\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-09-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Combinatorial Theory Series B\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0095895624000819\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Combinatorial Theory Series B","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0095895624000819","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
We study the generic volume-rigidity of -dimensional simplicial complexes in , and show that the volume-rigidity of a complex can be identified in terms of its exterior shifting. In addition, we establish the volume-rigidity of triangulations of several 2-dimensional surfaces and prove that, in all dimensions >1, volume-rigidity is not characterized by a corresponding hypergraph sparsity property.
期刊介绍：
The Journal of Combinatorial Theory publishes original mathematical research dealing with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series B is concerned primarily with graph theory and matroid theory and is a valuable tool for mathematicians and computer scientists.
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