Covering cross-polytopes with smaller homothetic copies
Let $ C_{n} $ be an $ n $-dimensional cross-polytope and $ \Gamma_{p}(C_{n}) $ be the smallest positive number $ \gamma $ such that $ C_{n} $ can be covered by $ p $ translates of $ \gamma C_{n} $. We obtain better estimates of $ \Gamma_{2^n}(C_n) $ for small $ n $ and a universal upper bound of $ \...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2024-01-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2024195?viewType=HTML |
| _version_ | 1827357997771259904 |
|---|---|
| author | Feifei Chen Shenghua Gao Senlin Wu |
| author_facet | Feifei Chen Shenghua Gao Senlin Wu |
| author_sort | Feifei Chen |
| collection | DOAJ |
| description | Let $ C_{n} $ be an $ n $-dimensional cross-polytope and $ \Gamma_{p}(C_{n}) $ be the smallest positive number $ \gamma $ such that $ C_{n} $ can be covered by $ p $ translates of $ \gamma C_{n} $. We obtain better estimates of $ \Gamma_{2^n}(C_n) $ for small $ n $ and a universal upper bound of $ \Gamma_{2^n}(C_n) $ for all positive integers $ n $. |
| first_indexed | 2024-03-08T05:56:19Z |
| format | Article |
| id | doaj.art-17622fa70dd34784916f2b092245aad2 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-08T05:56:19Z |
| publishDate | 2024-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-17622fa70dd34784916f2b092245aad22024-02-05T01:19:09ZengAIMS PressAIMS Mathematics2473-69882024-01-01924014402010.3934/math.2024195Covering cross-polytopes with smaller homothetic copiesFeifei Chen0 Shenghua Gao1Senlin Wu2School of Mathematics, North University of China, Taiyuan 030051, ChinaSchool of Mathematics, North University of China, Taiyuan 030051, ChinaSchool of Mathematics, North University of China, Taiyuan 030051, ChinaLet $ C_{n} $ be an $ n $-dimensional cross-polytope and $ \Gamma_{p}(C_{n}) $ be the smallest positive number $ \gamma $ such that $ C_{n} $ can be covered by $ p $ translates of $ \gamma C_{n} $. We obtain better estimates of $ \Gamma_{2^n}(C_n) $ for small $ n $ and a universal upper bound of $ \Gamma_{2^n}(C_n) $ for all positive integers $ n $.https://www.aimspress.com/article/doi/10.3934/math.2024195?viewType=HTMLconvex bodycovering functionalhadwiger's covering conjecturehomothetic copy |
| spellingShingle | Feifei Chen Shenghua Gao Senlin Wu Covering cross-polytopes with smaller homothetic copies AIMS Mathematics convex body covering functional hadwiger's covering conjecture homothetic copy |
| title | Covering cross-polytopes with smaller homothetic copies |
| title_full | Covering cross-polytopes with smaller homothetic copies |
| title_fullStr | Covering cross-polytopes with smaller homothetic copies |
| title_full_unstemmed | Covering cross-polytopes with smaller homothetic copies |
| title_short | Covering cross-polytopes with smaller homothetic copies |
| title_sort | covering cross polytopes with smaller homothetic copies |
| topic | convex body covering functional hadwiger's covering conjecture homothetic copy |
| url | https://www.aimspress.com/article/doi/10.3934/math.2024195?viewType=HTML |
| work_keys_str_mv | AT feifeichen coveringcrosspolytopeswithsmallerhomotheticcopies AT shenghuagao coveringcrosspolytopeswithsmallerhomotheticcopies AT senlinwu coveringcrosspolytopeswithsmallerhomotheticcopies |