期刊文献+

特殊凸体边界小位似体覆盖

Covering the Boundary of Special Convex Bodies with Smaller Homothetic Copies
下载PDF
导出
摘要 针对覆盖n维凸体K所需K的内部的平移的最小数目c(K)不超过2n的Hadwiger猜想,依据c(K)等于覆盖K的边界bdK所需K的位似系数相同的小位似体的最小数目这一核心结果,借鉴将c(K)的估值问题连续化的方法,研究了用m个K的位似系数相同的小位似体覆盖bdK所需最小位似系数γm(K)精确值的估算问题。得到了当K是正四面体时γ4(K)和γ8(K)的值以及当K是正八面体时γ6(K),γ7(K)和γ8(K)的值,并证明了当K是R^n中以n-1维凸体D为底的柱体时γ2n(K)=Γ2n(K)=Γ2n-1(D),其中Γm(K)表示用m个K的位似系数相同的小位似体覆盖K所需最小位似系数。 For Hadwiger conjecture that the least number c(K) of translates of the interior of K needed to cover K is at most 2 n , according to the fact that c(K) equals the least number of smaller homothetic copies of K with the same homothetic ratio needed to cover the boundary bd K of K , drawing on the continuous functional to estimate the value of c(K), studying the problem of estimating the value of the smallest homothetic ratio γ m(K) that bd K can be covered by m translates of γ m(K)K . The value of γ 4(K) and γ 8(K) when K is a regular tetrahedron, as well as the value of γ 6(K),γ 7(K) and γ 8(K) are obtained when K is a regular octahedron are obtained. It is proved that γ 2 n (K)=Γ 2 n (K)=Γ 2 n-1 (D) when K is a cylinder in R^n with the n -1 dimensional convex set D as the base, where Γ m(K) is the smallest value of the homothetic radio γ that K can be covered by m translates of γK .
作者 计东海 吕德晶 马泽敏 JI Dong-hai;LV De-jing;MA Ze-min(School of Sciences, Harbin University of Science and Technology,Harbin 150080,China)
出处 《哈尔滨理工大学学报》 CAS 北大核心 2019年第2期115-120,共6页 Journal of Harbin University of Science and Technology
基金 国家自然科学基金(11371114,11571085)
关键词 凸体 覆盖 小位似体 Hadwiger猜想 convex body covering smaller homothetic copy Hadwiger’s conjecture
  • 相关文献

参考文献4

二级参考文献33

  • 1ZONG Chuanming School of Mathematical Sciences,Peking University,Beijing 100871,China.A quantitative program for Hadwiger's covering conjecture[J].Science China Mathematics,2010,53(9):2551-2560. 被引量:8
  • 2Károly Bezdek.The illumination conjecture and its extensions[J]. Periodica Mathematica Hungarica . 2006 (1-2)
  • 3V. Boltyanski.Solution of the Illumination Problem for Bodies with md M = 2[J]. Discrete & Computational Geometry . 2001 (4)
  • 4H. Martini,V. Soltan.Combinatorial problems on the illumination of convex bodies[J]. Aequationes Mathematicae . 1999 (2-3)
  • 5Ioannis Papadoperakis.An Estimate for the Problem of Illumination of the Boundary of a Convex Body in E3[J]. Geometriae Dedicata . 1999 (3)
  • 6István Talata.Solution of Hadwiger-Levi’s Covering Problem for Duals of Cyclic 2k-Polytopes[J]. Geometriae Dedicata . 1999 (1)
  • 7Károly Bezdek,Tibor Bisztriczky.A Proof of Hadwiger’s Covering Conjecture for Dual Cyclic Polytopes[J]. Geometriae Dedicata . 1997 (1)
  • 8Chuanming Zong.Some remarks concerning kissing numbers, blocking numbers and covering numbers[J]. Periodica Mathematica Hungarica . 1995 (3)
  • 9Marek Lassak.Covering a plane convex body by four homothetical copies with the smallest positive ratio[J]. Geometriae Dedicata . 1986 (2)
  • 10Kurt Schütte.überdeckungen der Kugel mit h?chstens acht Kreisen[J]. Mathematische Annalen . 1955 (1)

共引文献8

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部