- Tiling-based models of perimeter and area

arXiv:1811.00082 - Discrete geometry for electoral geography
(with Moon Duchin)

arXiv:1808.05860 - The pinnacle set of a permutation
(with Robert Davis,
Sara
A. Nelson, and T. Kyle
Petersen)
*Discrete Mathematics*341 (2018), 3249-3270

arXiv:1704.05494 - Enumerations relating braid and commutation classes
(with Susanna Fishel, Elizabeth
Milićević, and Rebecca Patrias)
*European Journal of Combinatorics*74 (2018), 11-26

arXiv:1708.04372 - Poset edge densities, nearly reduced words, and barely set-valued
tableaux
(with Victor Reiner and Alexander Yong)
*Journal of Combinatorial Theory, Series A*158 (2018), 66-125

arXiv:1603.09589 - Parabolic
double cosets in Coxeter groups
(with Sara C. Billey,
Matjaž
Konvalinka, T. Kyle Petersen, and William Slofstra)
*The Electronic Journal of Combinatorics*25 (2018), P1.23

arXiv:1612.00736 - Rhombic tilings and Bott-Samelson varieties
(with Laura
Escobar, Oliver Pechenik, and Alexander Yong)
*Proceedings of the American Mathematical Society*146 (2018), 1921-1935

arXiv:1605.05613 - Prolific permutations and permuted packings: downsets containing many
large patterns
(with David
Bevan and Cheyne
Homberger)
*Journal of Combinatorial Theory, Series A*153 (2018), 98-121

arXiv:1608.06931 - Sorting permutations: games, genomes, and cycles
(with K.L.M. Adamyk, E. Holmes, G.R. Mayfield, D.J. Moritz, M. Scheepers, and H.C.
Wauck)

Discrete Mathematics, Algorithms and Applications, 9 (2017), Article 1750063

arXiv:1410.2353 - Reduced
word
manipulation: patterns and enumeration
*Journal of Algebraic Combinatorics*46 (2017), 189-217

arXiv:1503.05205 - Parabolic
double cosets in Coxeter groups (extended abstract)
(with Sara C. Billey, Matjaž Konvalinka,
T. Kyle Petersen, and William Slofstra)
*Discrete Mathematics and Theoretical Computer Science Proceedings, FPSAC 2016*, 2016, 275-286 - A balanced Diplomacy tournament
(with Andrew Ash, J. Marshall Ash, Timothy L. McMurry, and Allen J. Schwenk)
*Journal of Combinatorial Mathematics and Combinatorial Computing*96 (2016), 245-264 - Coincidence among families of mesh patterns
(with Anders Claesson and Henning Ulfarsson)
*The Australasian Journal of Combinatorics*63 (2015), 88-106

arXiv:1412.0703 - Intervals and factors in the Bruhat order
*Discrete Mathematics and Theoretical Computer Science*17 (2015), 383-396

arXiv:1303.3852 - The depth of a permutation
(with T. Kyle
Petersen)
*Journal of Combinatorics*6 (2015), 145-178

arXiv:1202.4765 - On the expected number of commutations in reduced words
*The Australasian Journal of Combinatorics*62 (2015), 147-154

arXiv:1407.5636 - How to write a permutation as a product of involutions (and why you
might care)
(with T. Kyle
Petersen)
*Integers*13 (2013), A63

arXiv:1202.5319 - Mesh
patterns with
superfluous mesh
*Advances in Applied Mathematics*51 (2013), 606-618

arXiv:1302.1883 - Coincidental pattern avoidance
*Journal of Combinatorics*4 (2013), 311-326

arXiv:1301.6096 - Fingerprint databases for theorems
(with Sara
C. Billey)
*Notices of the American Mathematical Society*60 (2013), 1034-1039

arXiv:1304.3866 - A
combinatorial proof of symmetry among minimal star
factorizations
*Discrete Mathematics*312 (2012), 2482-2490

arXiv:1109.4642 - Repetition in reduced decompositions
*Advances in Applied Mathematics*49 (2012), 1-14

arXiv:1106.2839 - Derangement frequency in the boolean complex
(with Kári
Ragnarsson)
*Raust*8 (2011), 43-46

arXiv:1104.0674 - Sort-invariant
non-messing-up
*The Electronic Journal of Combinatorics*18(1) (2011), P222

arXiv:1009.4201 - Homology of the boolean complex
(with Kári
Ragnarsson)
*Journal of Algebraic Combinatorics*34 (2011), 617-639

arXiv: 1005.4411 - Spotlight tiling
*Annals of Combinatorics*14 (2011), 553-568

arXiv: 0711.1819 - The γ-vector of a barycentric subdivision
(with Eran
Nevo and T. Kyle
Petersen)
*Journal of Combinatorial Theory, Series A*118 (2011), 1364-1380

arXiv: 1003.2544 - Boolean complexes for Ferrers graphs
(with Anders Claesson, Sergey Kitaev, and Kári
Ragnarsson)
*The Australasian Journal of Combinatorics*48 (2010), 159-173

arXiv: 0808.2307 - Boolean complexes and boolean numbers
*Discrete Mathematics and Theoretical Computer Science Proceedings, FPSAC 2010*, 2010, 1049-1056 - The Möbius function of the permutation pattern poset
(with Einar
Steingrímsson)
*Journal of Combinatorics*1 (2010), 39-52

arXiv: 0902.4011 - Partitioning a planar graph of girth ten into a forest and a matching
(with A. Bassa, J. Burns, J. Campbell, A. Deshpande, J.
Farley, M. Halsey, S.-Y. Ho,
D. J. Kleitman, S. Michalakis, P.-O. Persson, P. Pylyavskyy, L. Rademacher, A. Riehl, M. Rios, J. Samuel,
A. Vijayasarathy, and L. Zhao)
*Studies in Applied Mathematics*124 (2010), 213-228 - Obtainable sizes of topologies on finite sets
(with Kári
Ragnarsson)
*Journal of Combinatorial Theory, Series A*117 (2010), 138-151

arXiv: 0802.2550 - Domino tiling congruence modulo 4
*Graphs and Combinatorics*25 (2009), 625-638

arXiv: 0705.1300 - Optimizing linear extensions
*SIAM Journal on Discrete Mathematics*23 (2009), 1450-1454

arXiv: 0905.1688 - Homotopy type of the boolean complex of a Coxeter system
(with Kári
Ragnarsson)
*Advances in Mathematics*222 (2009), 409-430

arXiv: 0806.0906 - Relations on generalized degree sequences
(with Caroline J.
Klivans and Kathryn L.
Nyman)
*Discrete Mathematics*309 (2009), 4377-4383

arXiv: 0806.4012 - Pattern avoidance and the Bruhat order
*Journal of Combinatorial Theory, Series A*114 (2007), 888-905

arXiv: math/0604322 - A non-messing-up phenomenon for posets
*Annals of Combinatorics*11 (2007), 101-114

arXiv: math/0404396 - On expected factors in reduced decompositions in type
*B**European Journal of Combinatorics*28 (2007), 1144-1151

arXiv: math/0508153 - Reduced decompositions and permutation patterns
*Journal of Algebraic Combinatorics*24 (2006), 263-284

arXiv: math/0506242 - The combinatorics
of reduced decompositions

Ph.D. Thesis, Massachusetts Institute of Technology, 2006 - Tiling parity results and the holey square solution
*The Electronic Journal of Combinatorics*11(2) (2005), R17

arXiv: 0409105 - Database of
Permutation Pattern Avoidance
This is an online database of phenomena charaterized by the avoidance of finitely many permutation patterns. Patterns, phenomena, references, and any enumeration are all cross-listed and searchable.