On Grunbaum's conjecture about inner illumination of convex bodies

Authors
Boltyanski, V Martini, H Soltan, V
Citation
V. Boltyanski et al., On Grunbaum's conjecture about inner illumination of convex bodies, DISC COM G, 22(3), 1999, pp. 403-410
Citations number
9
Categorie Soggetti
Engineering Mathematics
Journal title
DISCRETE & COMPUTATIONAL GEOMETRY
ISSN journal
01795376 → ACNP
Volume
22
Issue
3
Year of publication
1999
Pages
403 - 410
Database
ISI
SICI code
0179-5376(199910)22:3<403:OGCAII>2.0.ZU;2-A
Abstract
In 1964 Grunbaum conjectured that any primitive set illuminating from withi n a convex body in E-d, d greater than or equal to 3, has at most 2(d) poin ts. This was confirmed by V. Soltan in 1995 for the case d = 3. Here we giv e a negative answer to Grunbaum's conjecture for all d greater than or equa l to 4, by constructing a convex body K subset of E-d with primitive illumi nating sets of an arbitrarily large cardinality.