Homothetic Covering of Crosspolytopes

Yunfang Lyu, Feifei Chen and Senlin Wu ()
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Yunfang Lyu: Department of Applied Mathematics, Harbin University of Science and Technology, Harbin 150080, China
Feifei Chen: School of Mathematics, North University of China, Taiyuan 030051, China
Senlin Wu: School of Mathematics, North University of China, Taiyuan 030051, China

Mathematics, 2025, vol. 13, issue 4, 1-23

Abstract: The exact value of Γ m ( K ) , which is the least positive number γ such that a convex body K can be covered by m translates of γ K , is usually difficult to obtain. We present exact values of Γ 14 ( B 1 3 ) , Γ 11 ( B 1 4 ) , Γ 2 n ( B 1 n ) , Γ 2 n + 1 ( B 1 n ) , and Γ 2 n + 2 ( B 1 n ) , where B 1 n is the unit ball of R n endowed with the taxicab norm.

Keywords: crosspolytope; Hadwiger’s covering conjecture; homothetic covering (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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