. Answering a question of F¨uredi and Loeb (1994), we show that the maximum number of pairwise intersecting homothets of a d -dimensional centrally symmetric convex body K , none of which contains the center of another in its interior, is at most O (3 d d log d ). If K is not necessarily centrally symmetric and the role of its center is played by its centroid, then the above bound can be replaced by O (3 d d log d ). We establish analogous results for the case where the center is defined as an arbitrary point in the interior of K . We also show that in the latter case, one can always find families of at least Ω((2 / √ 3) d ) translates of K with the above property.
． 回答F¨uredi和Loeb(1994)的一个问题，我们证明了d维中心对称凸体K的成对相交同形体的最大数量，其中任何一个都不包含另一个的中心在其内部，最多为O (3 d d log d)。如果K不一定是中心对称的，它的中心的作用由它的质心来扮演，那么上面的边界可以用O (3 d d log d)来代替。对于中心被定义为K内部任意点的情况，我们建立了类似的结果。我们还证明，在后一种情况下，人们总能找到至少Ω((2 /√3)d)的族，K的平移具有上述性质。
{"title":"WHAT IS A BODY?","authors":"","doi":"10.2307/j.ctv1s5nxr9.5","DOIUrl":"https://doi.org/10.2307/j.ctv1s5nxr9.5","url":null,"abstract":". Answering a question of F¨uredi and Loeb (1994), we show that the maximum number of pairwise intersecting homothets of a d -dimensional centrally symmetric convex body K , none of which contains the center of another in its interior, is at most O (3 d d log d ). If K is not necessarily centrally symmetric and the role of its center is played by its centroid, then the above bound can be replaced by O (3 d d log d ). We establish analogous results for the case where the center is defined as an arbitrary point in the interior of K . We also show that in the latter case, one can always find families of at least Ω((2 / √ 3) d ) translates of K with the above property.","PeriodicalId":151650,"journal":{"name":"Body Becoming","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132362797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"EMBODIMENT AS A VISION FOR DEMOCRACY","authors":"","doi":"10.2307/j.ctv1s5nxr9.17","DOIUrl":"https://doi.org/10.2307/j.ctv1s5nxr9.17","url":null,"abstract":"","PeriodicalId":151650,"journal":{"name":"Body Becoming","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130548125","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"THE POLITICS OF BODIES IN MOTION","authors":"","doi":"10.2307/j.ctv1s5nxr9.16","DOIUrl":"https://doi.org/10.2307/j.ctv1s5nxr9.16","url":null,"abstract":"","PeriodicalId":151650,"journal":{"name":"Body Becoming","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133325451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"THE HEALING POWER OF SOMATICS","authors":"","doi":"10.2307/j.ctv1s5nxr9.15","DOIUrl":"https://doi.org/10.2307/j.ctv1s5nxr9.15","url":null,"abstract":"","PeriodicalId":151650,"journal":{"name":"Body Becoming","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116274926","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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