A number of important results in combinatorics, discrete geometry, and theoretical computer
science have been proved using algebraic topology. While the results are quite famous …

Davenport Schinzel sequences are sequences that do not contain forbidden alternating
subsequences of certain length. They are a powerful combinatorial tool applicable in …

These lecture notes for the IAS/Park City Graduate Summer School in Geometric
Combinatorics (July 2004) provide an overview of poset topology. These notes include …

This book is a revised version of my 2005 thesis [71] for the degree of Doctor of Philosophy
at the Royal Institute of Technology (KTH) in Stockholm. The whole idea of writing a …

We prove an O (n (k+ 1) 1/3) upper bound for planar k-sets. This is the first considerable
improvement on this bound after its early solution approximately 27 years ago. Our proof …

We use the Laplacian and power method to compute Betti numbers of simplicial complexes.
This has a number of advantages over other methods, both in theory and in practice. It …

We discuss five fundamental results of discrete mathematics: the lemmas of Sperner and
Tucker from combinatorial topology and the theorems of Carathéodory, Helly, and Tverberg …

We give a simple lazy randomized incremental algorithm to compute≤ k-levels in
arrangements of x-monotone Jordan curves in the plane, and in arrangements of planes in …

The objective of this paper is to study the geometry of admissible rook configurations on a
general m× n chessboard. An admissible configuration is any non-taking placement of …

Point Selections and Weak ε-Nets for Convex Hulls Page 1 Combinatorics, Probability and
Computing (1992) 1, 189-200 Copyright © 1992 Cambridge University Press Point Selections …