THE DIFFERENT WAYS OF STABBING DISJOINT CONVEX-SETS

被引:28
作者
KATCHALSKI, M [1 ]
LEWIS, T [1 ]
LIU, A [1 ]
机构
[1] UNIV ALBERTA,DEPT MATH,EDMONTON T6G 2E1,ALBERTA,CANADA
关键词
D O I
10.1007/BF02187836
中图分类号
TP301 [理论、方法];
学科分类号
081202 ;
摘要
We construct a family of n disjoint convex set in R(d) having (n/(d - 1))d-1 geometric permutations. As well, we complete the enumeration problem for geometric permutations of families of disjoint translates of a convex set in the plane, settle the case for cubes in R(d), and construct a family of d + 1 translates in R(d) admitting (d + 1)!/2 geometric permutations.
引用
收藏
页码:197 / 206
页数:10
相关论文
共 10 条
[1]  
Danzer L., 1962, P S PURE MATH, V7, P101
[2]   THE MAXIMUM NUMBER OF WAYS TO STAB N-CONVEX NONINTERSECTING SETS IN THE PLANE IS 2N-2 [J].
EDELSBRUNNER, H ;
SHARIR, M .
DISCRETE & COMPUTATIONAL GEOMETRY, 1990, 5 (01) :35-42
[3]  
GRUNBAUM B, 1958, ARCH MATH, V9, P465
[4]  
Hadwiger H., 1964, COMBINATORIAL GEOMET
[5]   GEOMETRIC PERMUTATIONS FOR CONVEX-SETS [J].
KATCHALSKI, M ;
LEWIS, T ;
ZAKS, J .
DISCRETE MATHEMATICS, 1985, 54 (03) :271-284
[6]   GEOMETRIC PERMUTATIONS OF DISJOINT TRANSLATES OF CONVEX-SETS [J].
KATCHALSKI, M ;
LEWIS, T ;
LIU, A .
DISCRETE MATHEMATICS, 1987, 65 (03) :249-259
[7]   GEOMETRIC PERMUTATIONS AND COMMON TRANSVERSALS [J].
KATCHALSKI, M ;
LEWIS, T ;
LIU, A .
DISCRETE & COMPUTATIONAL GEOMETRY, 1986, 1 (04) :371-377
[8]   A CONJECTURE OF GRUNBAUM ON COMMON TRANSVERSALS [J].
KATCHALSKI, M .
MATHEMATICA SCANDINAVICA, 1986, 59 (02) :192-198
[9]   PROOF OF GRUNBAUM CONJECTURE ON COMMON TRANSVERSALS FOR TRANSLATES [J].
TVERBERG, H .
DISCRETE & COMPUTATIONAL GEOMETRY, 1989, 4 (03) :191-203
[10]   UPPER-BOUNDS ON GEOMETRIC PERMUTATIONS FOR CONVEX-SETS [J].
WENGER, R .
DISCRETE & COMPUTATIONAL GEOMETRY, 1990, 5 (01) :27-33