4 papers
An extension of the Moser-Tardos algorithmic local lemma
Wesley Pegden
A recent theorem of Bissacot, et al. proved using results about the cluster expansion in statistical mechanics extends the Lovász Local Lemma by weakening the conditions under whic…
A finite goal set in the plane which is not a Winner
Wesley Pegden
J. Beck has shown that if two players alternately select previously unchosen points from the plane, Player 1 can always build a congruent copy of any given finite goal set G, in sp…
Sets resilient to erosion
Wesley Pegden
The erosion of a set in Euclidean space by a radius r>0 is the subset of X consisting of points at distance >/-r from the complement of X. A set is resilient to erosion if it is si…
Highly nonrepetitive sequences: winning strategies from the local lemma
Wesley Pegden
We prove game-theoretic versions of several classical results on nonrepetitive sequences, showing the existence of winning strategies using an extension of the Lovász Local Lemma w…