{"title":"对称超平面排列特征多项式的计算","authors":"Taylor Brysiewicz, Holger Eble, Lukas Kühne","doi":"10.1007/s00454-023-00557-2","DOIUrl":null,"url":null,"abstract":"Abstract We introduce a new algorithm computing the characteristic polynomials of hyperplane arrangements which exploits their underlying symmetry groups. Our algorithm counts the chambers of an arrangement as a byproduct of computing its characteristic polynomial. We showcase our implementation, based on , on examples coming from hyperplane arrangements with applications to physics and computer science.","PeriodicalId":356162,"journal":{"name":"Discrete and Computational Geometry","volume":"3 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Computing Characteristic Polynomials of Hyperplane Arrangements with Symmetries\",\"authors\":\"Taylor Brysiewicz, Holger Eble, Lukas Kühne\",\"doi\":\"10.1007/s00454-023-00557-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We introduce a new algorithm computing the characteristic polynomials of hyperplane arrangements which exploits their underlying symmetry groups. Our algorithm counts the chambers of an arrangement as a byproduct of computing its characteristic polynomial. We showcase our implementation, based on , on examples coming from hyperplane arrangements with applications to physics and computer science.\",\"PeriodicalId\":356162,\"journal\":{\"name\":\"Discrete and Computational Geometry\",\"volume\":\"3 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-11-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete and Computational Geometry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s00454-023-00557-2\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete and Computational Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s00454-023-00557-2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Computing Characteristic Polynomials of Hyperplane Arrangements with Symmetries
Abstract We introduce a new algorithm computing the characteristic polynomials of hyperplane arrangements which exploits their underlying symmetry groups. Our algorithm counts the chambers of an arrangement as a byproduct of computing its characteristic polynomial. We showcase our implementation, based on , on examples coming from hyperplane arrangements with applications to physics and computer science.
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