Publications

Papers

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Abelian Sandpile

Stability of patterns in the Abelian sandpile (with Charles K. Smart)

Submitted. In the arXiv since August 30, 2017 Show Abstract

The Apollonian structure of integer superharmonic matrices (with Lionel Levine, Charles K. Smart)

Annals of Mathematics 186 (2017) 1-67. In the arXiv, updated July 17, 2017) Extra: Code to generate tiles.Show Abstract

Apollonian structure in the Abelian Sandpile (with Lionel Levine, Charles K. Smart)

GAFA 26 (2016) 306-336 (preprint available. In the arXiv, updated May 22, 2014) Extra: images of Γ on various lattices.Show Abstract

Convergence of the Abelian Sandpile (with Charles K. Smart)

Duke Math J. 162 (2013) 627-642. (preprint available. In the arXiv, updated March 7, 2012)Show Abstract

Fair division

A partisan districting protocol with provably nonpartisan outcomes (with Ariel Procaccia, Dingli Yu)

Submitted. In the arXiv since October 24, 2017. Show Abstract

Randomness

The distribution of minimum-weight cliques and other subgraphs
in graphs with random edge weights
(with Alan Frieze, Gregory Sorkin)

Submitted. In the arxiv, updated July 2017. Show Abstract

Constraining the clustering transition for colorings of sparse random graphs (with Michael Anastos, Alan Frieze)

Submitted. In the arxiv since May 2017. Show Abstract

Diffusion limited aggregation in the Boolean lattice (with Alan Frieze)

Submitted. In the arxiv since May 2017. Show Abstract

Assessing significance in a Markov chain without mixing (with Maria Chikina, Alan Frieze)

PNAS 114 (2017) 2860-2864 (also: arXiv) Extra: Code for redistricting chain. Extra: Brief amici curiae in SCOTUS Gill v. Whitford gerrymandering case Show Abstract

Minors of a random binary matroid (with Colin Cooper, Alan Frieze)

Submitted. In the arXiv since December 7, 2016. Show Abstract

Online purchasing under uncertainty (with Alan Frieze)

Random Structures & Algorithms (Accepted). In the arXiv since May 19, 2016. Show Abstract

Looking for vertex number one (with Alan Frieze)

Annals of Applied Probability 27 (2017) 582-630. Also in the arXiv, last updated May 2016. Show Abstract

Scalefree hardness of average-case Euclidean TSP approximation (with Alan Frieze)

Submitted. In the arXiv since April 15, 2016. Show Abstract

Separating subadditive Euclidean functionals (with Alan Frieze)

STOC 2016. Journal version in Random Structures & Algorithms 51 (2017) 375-403. In the arXiv since January 8, 2015. Show Abstract

Traveling in randomly embedded random graphs (with Alan Frieze)

RANDOM 2017. In the arXiv since November 24, 2014. Extra: Code for Figure 1. Show Abstract

Between 2- and 3-colorability (with Alan Frieze)

Electronic Journal of Combinatorics 22 #P1.34. In the arXiv since April 19, 2014. Extra: bound.cpp. Show Abstract

An extension of the Moser-Tardos algorithmic local lemma

SIAM J. Discrete Math 28 911-917 (2014). (preprint available, last updated January 26, 2013) Show Abstract

The Lefthanded Local Lemma characterizes chordal dependency graphs

Random Structures 41 (2012) 546-556. In the arXiv since April 2012. Show Abstract

Highly nonrepetitive sequences: winning strategies from the Local Lemma

Random Structures & Algorithms 38 pp 140-161 (preprint also available, last updated October 24, 2010) Show Abstract

Graph Theory

Critical graphs without triangles: an optimum density construction

Combinatorica 33 (4) (2013) 495-513 (preprint also available) Show Abstract

Distance Sequences in Locally Infinite Vertex-Transitive Digraphs

Combinatorica 26 (5) (2006) 577-585 (pdf is also available) Show Abstract

Geometry

Sets resilient to erosion

Advances in Geometry 11 (2011) pp. 201-224. (preprint is available) Show Abstract

Games

(see also the RSA 38 paper, above)

Walker-Breaker games (with Lisa Espig, Alan Frieze, Michael Krivelevich )

SIAM J. Discrete Math. 29 (2015). In the arXiv since January 22, 2014. (A preprint is also available.) Show Abstract

The topology of competitively constructed graphs (with Alan Frieze)

The Electronic Journal of Combinatorics 21 #P2.26, In the arXiv since December 3, 2013. (A preprint is also available.) Show Abstract

The Hales-Jewett number is exponential: game-theoretic consequences (with J. Beck and S. Vijay)

Analytic Number Theory: Essays in Honour of Klaus Roth
(Editors: William Chen, Tim Gowers, Heini Halberstam, Wolfgang Schmidt and Bob Vaughan) (A preprint is also available.) Show Abstract

A finite goal set in the plane which is not a winner

Discrete Mathematics 308 (24) (2008) 6546-6551 (pdf also available) Show Abstract