# 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

#### 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.

#### 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.

#### 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)

### Fair division

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

Submitted. In the arXiv since October 24, 2017.

### Extremal problems

#### Extremal Collections of k-Uniform Vectors (with Joseph Briggs)

Submitted. In the arXiv since January 2018.

### Randomness

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

Accepted to Annals of Applied Probability. In the arXiv, updated December 2017.

#### A note on dispersing particles on a line (with Alan Frieze)

Submitted. In the arXiv since November 2017.

#### A note on the localization number of random graphs: diameter two case (with Andrzej Dudek, Alan Frieze)

Submitted. In the arXiv since December 2017.

#### 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.

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

Submitted. In the arXiv since May 2017.

#### 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

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

Submitted. In the arXiv since December 7, 2016.

#### Online purchasing under uncertainty (with Alan Frieze)

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

#### Looking for vertex number one (with Alan Frieze)

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

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

Submitted. In the arXiv since April 15, 2016.

#### 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.

#### Traveling in randomly embedded random graphs (with Alan Frieze)

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

#### 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.

#### An extension of the Moser-Tardos algorithmic local lemma

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

#### The Lefthanded Local Lemma characterizes chordal dependency graphs

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

#### Highly nonrepetitive sequences: winning strategies from the Local Lemma

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

### Graph Theory

#### Distance Sequences in Locally Infinite Vertex-Transitive Digraphs

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

### Geometry

#### Sets resilient to erosion

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

### 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.)

#### 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.)

#### 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.)