AbstractWe prove that a suitably separated family ofncompact convex sets inRdcan be met byk-flat transversals in at mostO(k)d2<//SUP> ((2k+1−2<//SUP>k)(nk+1))k(d−k), or for fixedkandd,O(nk(k+1)(d−k)) different order types. This is the first non-trivial upper bound for 1<k<d−1, and generalizes (asymptotically) the best upper bounds known for line transversals inR,d>2
According to a classical result of Grünbaum, the transversal number τ(F) of any family F of pairwis...
We show that a set of n disjoint unit spheres in R d admits at most two distinct geometric permutati...
We show that a set of n disjoint unit spheres in R d admits at most two distinct geometric permutati...
AbstractLet S be a family of n translates of a centrally symmetric convex set in the plane such that...
AbstractA geometric permutation is the pair of permutations formed by a common transversal for a fin...
We prove that the maximum number of geometric permutations, induced by line transversals to a collec...
AbstractLet S be a family of n translates of a centrally symmetric convex set in the plane such that...
AbstractWe introduce a new notion of ‘neighbors’ in geometric permutations. We conjecture that the m...
Abstract. We prove that the maximum number of geometric permutations, induced by line transversals t...
SIGLECNRS 17660 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc
AbstractWe introduce a new notion of ‘neighbors’ in geometric permutations. We conjecture that the m...
A family ? of sets satisfies the (p,q)-property if among every p members of ?, some q can be pierced...
Consider the following fundamental geometric problem: given a family of convex sets in the plane, do...
AbstractWe prove that a collection of compact convex sets of bounded diameters in Rd that is unbound...
We investigate a number of questions, problems, and conjectures related to geometric transversal the...
According to a classical result of Grünbaum, the transversal number τ(F) of any family F of pairwis...
We show that a set of n disjoint unit spheres in R d admits at most two distinct geometric permutati...
We show that a set of n disjoint unit spheres in R d admits at most two distinct geometric permutati...
AbstractLet S be a family of n translates of a centrally symmetric convex set in the plane such that...
AbstractA geometric permutation is the pair of permutations formed by a common transversal for a fin...
We prove that the maximum number of geometric permutations, induced by line transversals to a collec...
AbstractLet S be a family of n translates of a centrally symmetric convex set in the plane such that...
AbstractWe introduce a new notion of ‘neighbors’ in geometric permutations. We conjecture that the m...
Abstract. We prove that the maximum number of geometric permutations, induced by line transversals t...
SIGLECNRS 17660 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc
AbstractWe introduce a new notion of ‘neighbors’ in geometric permutations. We conjecture that the m...
A family ? of sets satisfies the (p,q)-property if among every p members of ?, some q can be pierced...
Consider the following fundamental geometric problem: given a family of convex sets in the plane, do...
AbstractWe prove that a collection of compact convex sets of bounded diameters in Rd that is unbound...
We investigate a number of questions, problems, and conjectures related to geometric transversal the...
According to a classical result of Grünbaum, the transversal number τ(F) of any family F of pairwis...
We show that a set of n disjoint unit spheres in R d admits at most two distinct geometric permutati...
We show that a set of n disjoint unit spheres in R d admits at most two distinct geometric permutati...