2 citations · 2 across the 2 of their papers we have counts for
4 papers
Lower bounds on geometric Ramsey functions
Marek Eliáš, Jiří Matoušek, Edgardo Roldán-Pensado +1
We continue a sequence of recent works studying Ramsey functions for semialgebraic predicates in . A -ary semialgebraic predicate on $\mathbb{R…
Simplifying inclusion-exclusion formulas
Xavier Goaoc, Jiří Matoušek, Pavel Paták +2
Let be a family of sets on a ground set , such as a family of balls in . For every finite measure on , such that t…
Unit Distances in Three Dimensions
Haim Kaplan, Jiri Matousek, Zuzana Safernova +1
We show that the number of unit distances determined by n points in R^3 is O(n^{3/2}), slightly improving the bound of Clarkson et al. established in 1990. The new proof uses the r…
On the nonexistence of k-reptile tetrahedra
Jiří Matoušek, Zuzana Safernová
A d-dimensional simplex S is called a k-reptile if it can be tiled without overlaps by simplices S_1,S_2,...,S_k that are all congruent and similar to S. For d=2, k-reptile simplic…