3 citations · 4 across the 8 of their papers we have counts for
5 papers · 1 filter
Erdos-Hajnal Sets and Semigroup Decompositions
Joshua N. Cooper
Define a set of lines in to be ``stacked'' with respect to if, from a vantage point far away in the direction of , the lines are linearly ordered by the ``cros…
Collinear Points in Permutations
J. Cooper, J. Solymosi
Consider the following problem: how many collinear triples of points must a transversal of (Z/nZ)^2 have? This question is connected with venerable issues in discrete geometry. We…
A Permutation Regularity Lemma
Joshua N. Cooper
We introduce a permutation analogue of the celebrated Szemeredi Regularity Lemma, and derive a number of consequences. This tool allows us to provide a structural description of pe…
Generalized de Bruijn Cycles
Joshua N. Cooper, Ronald L. Graham
For a set of integers , we define a -ary -cycle to be a assignment of the symbols 1 through to the integers modulo so that every word appears on some translate o…
Simulating a Random Walk with Constant Error
Joshua N. Cooper, Joel Spencer
We analyze Jim Propp's P-machine, a simple deterministic process that simulates a random walk on to within a constant. The proof of the error bound relies on several estimate…