Blocking numbers and fixing numbers of convex bodies

Abstract

In the present paper we study the blocking number of a convex body. We determine the blocking number of the crosspolytope in E 3 . We also estimate that the blocking number of the l p unit ball in E 3 is at most 6, for ln 3 ln 2 < p < + ∞ . For a d -dimensional cylinder H whose base is a ( d − 1 ) -dimensional convex body K , we obtain a lower bound and an upper bound of its blocking number in terms of the Hadwiger covering number and the blocking number of K respectively. Moreover, we introduce and study the fixing number of a convex body, we determine the exact lower and upper bounds of fixing numbers for all d -dimensional convex bodies.