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Homothetic Covering of Crosspolytopes

Author

Listed:
  • Yunfang Lyu

    (Department of Applied Mathematics, Harbin University of Science and Technology, Harbin 150080, China
    These authors contributed equally to this work.)

  • Feifei Chen

    (School of Mathematics, North University of China, Taiyuan 030051, China
    These authors contributed equally to this work.)

  • Senlin Wu

    (School of Mathematics, North University of China, Taiyuan 030051, China
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Yunfang Lyu & Feifei Chen & Senlin Wu, 2025. "Homothetic Covering of Crosspolytopes," Mathematics, MDPI, vol. 13(4), pages 1-23, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:4:p:546-:d:1585703
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    References listed on IDEAS

    as
    1. Man Yu & Yafang Lv & Yanping Zhao & Chan He & Senlin Wu, 2023. "Estimations of Covering Functionals of Convex Bodies Based on Relaxation Algorithm," Mathematics, MDPI, vol. 11(9), pages 1-15, April.
    Full references (including those not matched with items on IDEAS)

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