{"title":"超立方体的球分解","authors":"R. Hammack, P. C. Kainen","doi":"10.26493/2590-9770.1285.fd8","DOIUrl":null,"url":null,"abstract":"For d ≡ 1 or 3 (mod 6), the 2-skeleton of the d-dimensional hypercube is decomposed into the union of pairwise face-disjoint isomorphic 2-complexes, each a topological sphere. If d = 5, then such a decomposition can be achieved, but with non-isomorphic spheres.","PeriodicalId":236892,"journal":{"name":"Art Discret. Appl. Math.","volume":"104 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Sphere decompositions of hypercubes\",\"authors\":\"R. Hammack, P. C. Kainen\",\"doi\":\"10.26493/2590-9770.1285.fd8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For d ≡ 1 or 3 (mod 6), the 2-skeleton of the d-dimensional hypercube is decomposed into the union of pairwise face-disjoint isomorphic 2-complexes, each a topological sphere. If d = 5, then such a decomposition can be achieved, but with non-isomorphic spheres.\",\"PeriodicalId\":236892,\"journal\":{\"name\":\"Art Discret. Appl. Math.\",\"volume\":\"104 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-08-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Art Discret. Appl. Math.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.26493/2590-9770.1285.fd8\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Art Discret. Appl. Math.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.26493/2590-9770.1285.fd8","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
For d ≡ 1 or 3 (mod 6), the 2-skeleton of the d-dimensional hypercube is decomposed into the union of pairwise face-disjoint isomorphic 2-complexes, each a topological sphere. If d = 5, then such a decomposition can be achieved, but with non-isomorphic spheres.
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