Publications and coauthors

Below is a list of my publications and a list of my coauthors with links to their web pages. Click the title of a paper to download it as a PDF.


  • The Surprising Mathematics of Longest Increasing Subsequences. Cambridge University Press, 2015. Visit the book home page for a downloadable manuscript and more information.


  1. The oriented swap process and last passage percolation (joint with Elia Bisi, Fabio Deelan Cunden and Shane Gibbons). Preprint, 2020. See here for a Mathematica companion file. (This paper is the full version of the extended abstract "Sorting networks, staircase Young tableaux and last passage percolation" listed below.)
  2. Absorbing time asymptotics in the oriented swap process (joint with Alexey Bufetov and Vadim Gorin). Preprint, 2020.


Journal papers

  1. Orthogonal polynomial expansions for the Riemann xi function in the Hermite, Meixner-Pollaczek, and continuous Hahn bases. To appear in Acta Arithmetica.
    Note: this paper exists in two different versions with different titles. See this page for additional information and related resources.
  2. Alternative summation orders for the Eisenstein series G2 and Weierstrass ℘-function (joint with Robert Scherer). To appear in Rocky Mountain J. Math.
  3. The Taylor coefficients of the Jacobi theta constant θ3.  Ramanujan Journal. 52 (2020), 275--290. See here for a Maple package written by Doron Zeilberger that implements some of the formulas in the paper.
  4. Improved upper bounds in the moving sofa problem. With Yoav Kallus. Adv. Math. 340 (2018), 960-982. See here for the SofaBounds companion software package.
  5. Differential equations and exact solutions in the moving sofa problem. Experimental Math 27 (2018), 316-330. See below for a Mathematica companion file.
  6. On the number of n-dimensional representations of SU(3), the Bernoulli numbers, and the Witten zeta function. Acta Arithmetica 180 (2017), 111-159. See below for a Mathematica companion file.
  7. Bijective combinatorial proof of the commutation of transfer matrices in the dense O(1) loop model. With Ron Peled. Séminaire Lotharingien de Combinatoire. 73 (2015), B73b.
  8. Limit shapes of bumping routes in the Robinson-Schensted correspondence. With Piotr Sniady. Random Struct. Algor. 48 (2016), 171-182.
  9. Connectivity patterns in loop percolation I: the rationality phenomenon and constant term identities. Commun. Math. Phys. 330 (2014), 499-538.
  10. Jeu de taquin dynamics on infinite Young tableaux and second class particles. With Piotr Sniady. Ann. Probab. 43 (2015), 682-737.
  11. New enumeration formulas for alternating sign matrices and square ice partition functions. With Arvind Ayyer. Adv. Math. 235 (2013), 161-186. (See below for 2 companion files.)
  12. Arctic circles, domino tilings and square Young tableauxAnn. Probab. 40 (2012), 611-647.
  13. Phase transitions in gravitational allocation. With Sourav Chatterjee, Ron Peled and Yuval Peres. Geom. Funct. Anal. 20 (2010), 870-917.
  14. A formula for a doubly refined enumeration of alternating sign matrices. With Matan Karklinsky. Adv. Appl. Math. 45 (2010), 28-35.
  15. More refined enumerations of alternating sign matrices. With Ilse Fischer. Adv. Math. 222 (2009), 2004-2035. (See below for companion file.)
  16. The oriented swap process. With Omer Angel and Alexander Holroyd. Ann. Probab. 37 (2009), 1970-1998.
  17. Enumeration formulas for Young tableaux in a diagonal strip. With Yuliy Baryshnikov. The Israel J. of Math. 178 (2010), 157-186.
  18. Gravitational allocation to Poisson points. With Sourav Chatterjee, Ron Peled and Yuval Peres. Annals of Math. 172 (2010), 617-671.
  19. Random sorting networks. With Omer Angel, Alexander Holroyd and Balint Virag. Adv. Math. 215 (2007), 839-868.
  20. The dynamics of Pythagorean triplesTrans. Amer. Math. Soc. 360 (2008), 6045-6064.
  21. Integrals, probability, and MacMahon’s theorem. With George Andrews, Henrik Eriksson and Fedor Petrov. J. Comb. Theory Ser. A 114 (2007), 545-554.
  22. Universal finitary codes with exponential tails. With Nate Harvey, Alexander Holroyd and Yuval Peres. Proc. London Math. Soc. 94 (2007), 475-496.
  23. Shortest paths in the Tower of Hanoi graph and finite automataSIAM J. Disc. Math. 20 (2006), 610-622.
  24. The number of guillotine partitions in d dimensions. With Eyal Ackerman, Gill Barequet and Ron Pinter. Inform. Proc. Lett. 98 (2006), 162-167.
  25. Random walks with k-wise independent increments. With Itai Benjamini and Gady Kozma. Elec. Comm. Prob. 11 (2006), 100-107.
  26. Limit shapes for random square Young tableaux. With Boris Pittel. Adv. Appl. Math. 38 (2007), 164-209.
  27. Permutations with short monotone subsequencesAdv. Appl. Math. 37 (2006), 501-510. An extended abstract also appeared in Proceedings of EuroComb 2005, Discr. Math. Theor. Comp. Sci. Proceedings Series Volume AE, 57-62.
  28. Waiting for a bat to fly by (in polynomial time). With Itai Benjamini, Gady Kozma, Laszlo Lovasz and Gabor Tardos. Comb., Prob. and Computing 15 (2006), 673-683.
  29. Roots of the derivative of a polynomialAmer. Math. Monthly 112 (2005), 66-68.
  30. Some formulas for the central trinomial and Motzkin numbersJ. of Integer Sequences 6 (2003), article 03.2.3.
  31. The number of steps in the Robinson-Schensted algorithmFunct. Anal. Appl. 39 (2005), 152-155.
  32. On distributions computable by random walks on graphs. With Guy Kindler. SIAM J. Disc. Math. 17 (2004), 624-633. Also appeared in Proc. of the Fifteenth ACM-SIAM Symposium on Discrete Algorithms (SODA04), 124-131.
  33. Integrals, partitions and cellular automata. With Alexander Holroyd and Thomas Liggett. Trans. Amer. Math. Soc. 356 (2004), 3349-3368.
  34. Partitions of n into t n^1/2 partsEurop. J. Combin. 26 (2005), 1-17.
  35. Explicit formulas for hook walks on continual Young diagramsAdv. Appl. Math. 32 (2004), 625-654.
  36. Projecting the surface measure of the sphere of l_p^n. With Assaf Naor. Ann. Inst. Henri Poincare Prob. Stat. 39 (2003), 241-261.
  37. Some comments on Euler’s series for pi^2/6Math. Gazette, July 2002, 281-284.
  38. Stirling’s approximation for n!: the ultimate short proof? Amer. Math. Monthly 107 (2000), 556-557.
  39. Sharp entropy bounds for discrete statistical simulationStatist. Probab. Lett. 42 (1999), 219-227.

Publications in conference proceedings

An unpublication (a paper I wrote but never published) 


Companion files

  • A Mathematica package OrientedSwaps. Companion to the paper "Staircase Young tableaux, sorting networks and last passage percolation" with Elia Bisi, Fabio Cunden and Shane Gibbons.
  • A software package SofaBounds (command line tool, written in C++). Companion to the paper "Improved upper bounds in the moving sofa problem" with Yoav Kallus.
  • A Mathematica package MovingSofas. Companion to the paper "Differential equations and exact solutions in the moving sofa problem". If you don't have Mathematica, you can download the PDF version.
  • A Mathematica notebook SU3-ASYM.nb. Companion to the paper "On the number of n-dimensional representations of SU(3), the Witten zeta function, and the Bernoulli numbers". If you don't have Mathematica, you can download the PDF version.
  • A Maple package RefinedASM1234.txt. Companion to the paper "New enumeration formulas for alternating sign matrices and square ice partition functions" with Arvind Ayyer.
  • A Mathematica notebook GammaDelta.nb. Companion to the paper "New enumeration formulas for alternating sign matrices and square ice partition functions" with Arvind Ayyer. This notebook verifies a claim added in the revised version of the paper.
  • A Mathematica notebook RefinedASM.nb. Companion to the paper "More refined enumerations of alternating sign matrices" with Ilse Fischer.


Eyal AckermanGeorge AndrewsOmer AngelArvind AyyerGill BarequetYuliy Baryshnikov, Itai Benjamini, Elia Bisi, Alexey BufetovSourav Chatterjee, Fabio Deelan CundenHenrik ErikssonIlse Fischer, Vadim Gorin, Nate Harvey, Alexander Holroyd, Shane Gibbons, Yoav KallusGuy KindlerGady KozmaThomas LiggettLaszlo Lovasz, Matan Karklinsky, Assaf NaorRon PeledYuval Peres, Fedor PetrovRon PinterBoris Pittel, Robert Scherer, Piotr ŚniadyGabor TardosBálint Virág