{"title":"根据多宽度对宽度为 1 的晶格四面体进行分类","authors":"Girtrude Hamm","doi":"10.1007/s00454-024-00659-5","DOIUrl":null,"url":null,"abstract":"<p>We introduce the multi-width of a lattice polytope and use this to classify and count all lattice tetrahedra with multi-width <span>\\((1,w_2,w_3)\\)</span>. The approach used in this classification can be extended into a computer algorithm to classify lattice tetrahedra of any given multi-width. We use this to classify tetrahedra with multi-width <span>\\((2,w_2,w_3)\\)</span> for small <span>\\(w_2\\)</span> and <span>\\(w_3\\)</span> and make conjectures about the function counting lattice tetrahedra of any multi-width.</p>","PeriodicalId":50574,"journal":{"name":"Discrete & Computational Geometry","volume":"74 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Classification of Width 1 Lattice Tetrahedra by Their Multi-Width\",\"authors\":\"Girtrude Hamm\",\"doi\":\"10.1007/s00454-024-00659-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We introduce the multi-width of a lattice polytope and use this to classify and count all lattice tetrahedra with multi-width <span>\\\\((1,w_2,w_3)\\\\)</span>. The approach used in this classification can be extended into a computer algorithm to classify lattice tetrahedra of any given multi-width. We use this to classify tetrahedra with multi-width <span>\\\\((2,w_2,w_3)\\\\)</span> for small <span>\\\\(w_2\\\\)</span> and <span>\\\\(w_3\\\\)</span> and make conjectures about the function counting lattice tetrahedra of any multi-width.</p>\",\"PeriodicalId\":50574,\"journal\":{\"name\":\"Discrete & Computational Geometry\",\"volume\":\"74 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-06-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete & Computational Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00454-024-00659-5\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete & Computational Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00454-024-00659-5","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
Classification of Width 1 Lattice Tetrahedra by Their Multi-Width
We introduce the multi-width of a lattice polytope and use this to classify and count all lattice tetrahedra with multi-width \((1,w_2,w_3)\). The approach used in this classification can be extended into a computer algorithm to classify lattice tetrahedra of any given multi-width. We use this to classify tetrahedra with multi-width \((2,w_2,w_3)\) for small \(w_2\) and \(w_3\) and make conjectures about the function counting lattice tetrahedra of any multi-width.
期刊介绍：
Discrete & Computational Geometry (DCG) is an international journal of mathematics and computer science, covering a broad range of topics in which geometry plays a fundamental role. It publishes papers on such topics as configurations and arrangements, spatial subdivision, packing, covering, and tiling, geometric complexity, polytopes, point location, geometric probability, geometric range searching, combinatorial and computational topology, probabilistic techniques in computational geometry, geometric graphs, geometry of numbers, and motion planning.
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