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Post-Doc at LaBRI, Université de Bordeaux and IDP, Université de Tours, France.
Research teams : SPACE (IDP), CEA (LaBRI).

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Andrew Elvey Price
LaBRI, Université de Bordeaux
33400 Talence, France


Research

I am currently a Post-Doc based at LaBRI, Université de Bordeaux, supervised by Mireille Bousquet-Mélou (Bordeaux) and Kilian Raschel (Tours). My research interests lie in all areas of enumerative combinatorics and in particular, interactions with probability theory and statistical mechanics. Combinatorial objects that I have studied include decorated planar maps, permutation patterns, lattice paths (mostly two dimensional), self-avoiding walks and directed acyclic graphs (DAGs). I have also investigated the question of when counting sequences are Stieltjes moment sequences.

My current research is largely focused on solving combinatorial functional equations in terms of Jacobi theta functions, a method that has proven effective for numerous systems of functional equations involving two catalytic variables. Here are slides for a short course on this subject that I gave to the combinatorics group in Bordeaux: [1][2][3][4].


Theses


Journal Publications

  • Compacted binary trees admit a stretched exponential
    With Wenjie Fang and Michael Wallner
    Journal of Combinatorial theory A (to appear) arXiv:1908.11181
  • The generating function of planar Eulerian orientations
    With Mireille Bousquet-Mélou
    Journal of Combinatorial theory A 172 (2020): 105183 arXiv:1803.08265
  • Numerical studies of Thompson’s group F and related groups
    With Tony Guttmann
    International Journal of Algebra and Computation 29(2): 179-243 (2019) Vol. 321 p34569-34578. arXiv:1706.07571
  • A structural characterisation of Av(1324) and new bounds on its growth rate
    With David Bevan, Robert Brignall and Jay Pantone
    European Journal of Combinatorics: Eurocomb 2017 special issue (to appear) arXiv:1711.10325
  • Counting Planar Eulerian Orientations
    With Tony Guttmann
    European Journal of combinatorics 71 (2018): 73-98 arXiv:1707.09120
  • The isoperimetric number of the incidence graph of PG(n,q)
    With Muhammad Adib Surani and Sanming Zhou
    Electronic Journal of Combinatorics 25.3 (2018), 3-20. arXiv:1612.03293
  • Permutations sortable by two stacks in series
    With Tony Guttmann
    Advances in applied mathematics (2017): 81-96. arXiv:1510.08663
  • Permutations sortable by deques and by two stacks in parallel
    With Tony Guttmann
    European Journal of Combinatorics 59 (2017): 71-95. arXiv:1508.02273
  • Off-critical parafermions and the winding angle distribution of the O(n) model
    With Jan De Gier, Tony Guttmann and Alexander Lee
    Journal of Physics A: Mathematical and Theoretical 45 (2012) 275002. arXiv:1203.2959

Conference publications

  • Asymptotics of minimal deterministic finite automata recognizing a finite binary language
    With Wenjie Fang and Michael Wallner
    AofA 2020. Proceedings of the 31st International Conference Probabilistic, Combinatorial and Asymptotic methods for the analysis of algorithms. (to appear)
  • Counting lattice walks by winding angle
    FPSAC 2020. Proceedings of the 32nd conference on Formal Power Series and Algebraic Combinatorics (to appear). arXiv:2003.01740
  • Eulerian orientations and the six-vertex model on planar maps
    With Mireille Bousquet-Mélou and Paul Zinn-Justin
    Proceedings of the 31st conference on Formal Power Series and Algebraic Combinatorics. Vol. 82B. Sém. Lothar. Combin. Article#70 (2019). arXiv:1902.07369
  • Staircases, dominoes and the growth rate of 1324-avoiders
    With David Bevan, Robert Brignall and Jay Pantone
    Proceedings of the European conference on combinatorics, graph theory and applications. Vol 61. Electronic notes in discrete mathematics (2017): 123-129.

Preprints and Submissions

  • Stieltjes moments sequences for pattern-avoiding permutations
    With Alin Bostan, Tony Guttmann and Jean-Marie Maillard
    arXiv:2001.00393 (2020)
  • Phylogenetic trees, augmented perfect matchings and a Thron-type continued fraction (T-fraction) for the Ward polynomials
    With Alan Sokal
    arXiv:2001.01468 (2020)
  • Counting lattice walks by winding angle
    Submitted to a conference (2019)
  • Permutations sortable by deques and two stacks in parallel share the same growth rate
    arXiv:1912.00056 (2019)
  • A Cayley graph for F_2×F_2 which is not minimally almost convex
    arXiv:1611.00101 (2016)

Articles in preparation

  • The stationary distribution of reflected Brownian motion in a cone: differential properties of the Laplace tranform
    With Mireille Bousquet-Mélou, Sandro Franceschi, Charlotte Hardouin and Kilian Raschel
  • The six vertex model on planar maps
    With Paul Zinn-Justin
  • Counting lattice walks by winding angle
  • Generating functions for the six vertex model on maps and Eulerian orientations by edges and vertices
    With Mireille Bousquet-Mélou
  • A new bijection for Mortimer-Prellberg walks and higher dimensional analogues
    With Julien Courtiel and Irène Marcovici
  • Discrete height functions on random quadrangulations
  • Theta function solution for properly coloured triangulations

Invited talks at conferences

  • Counting planar maps equipped with a height function
    Recent advances in loop models and height functions, Fribourg, Switzerland, September 2019 [slides]
  • Eulerian orientations and the six-vertex model on planar maps
    Journées Cartes, Université Paris Diderot, France, February 2019
  • Exact enumeration of planar Eulerian orientations
    Workshop on Enumerative Combinatorics, Oberwolfach, Germany, May 2018
  • Staircases and dominoes: Bounding the growth rate of 1324-avoiding permutations
    Journées de combinatoire de Bordeaux, Université de Bordeaux, France, February 2018 [slides]
  • Thompson’s group is probably not amenable
    Workshop on the Thompson’s groups, Odense, Denmark, August 2016 [slides]

Other talks at conferences

  • Eulerian orientations and the six vertex model on planar maps
    31st conference on formal power series and algebraic combinatorics (FPSAC), Ljubljana, Slovenia, July 2019 [slides]
  • Exact enumeration of weighted Eulerian orientations using Jacobi theta functions
    ALEA young, Normandy, France, May 2019 [slides]
  • Exact enumeration of planar Eulerian orientations
    Jounées ALEA, CIRM, Luminy, France, March 2018 [slides]
  • Permutations sortable by deques and two stacks in parallel
    Permutations patterns conference, Reykjavik, Iceland, June 2017 [slides]
  • A Cayley graph for F_2×F_2 which is not minimally almost convex
    Victorian algebra conference, La Trobe University, Melbourne, Australia, December 2016

Talks in seminars

  • Counting lattice walks using elliptic functions
    Séminaire de probabilités, UMPA, Lyon, France (by videoconference), April 2020.
  • Combinatorial functional equations and Jacobi theta functions
    Seminaire de combinatoire, LIPN, Paris, France (by videoconference), April 2020.
  • Counting lattice walks by winding angle using Jacobi theta
    functions

    Seminaire Combinatoire, IRIF, Paris, France (by videoconference), April 2020.
  • Counting lattice walks by winding angle using Jacobi theta functions
    Initial meeting of the ANR Project De rerum natura, INRIA Saclay, France, February 2020.
  • Stretched exponentials for compacted binary trees and a class of minimal automata
    Talk with Michael Wallner
    Seminaire Algo, LIGM, Marne-la-Vallée, France, January 2020.
  • Stretched exponentials for compacted binary trees and a class of minimal automata
    Talk with Michael Wallner
    Groupe de travail de combinatoire énumérative et algébraic, LaBRI, Université de Bordeaux, France, December 2019.
  • Eulerian orientations and the six vertex model on planar maps
    Combinatoire et interactions, IHP, Paris, France, May 2019.
  • Eulerian orientations and the six-vertex model on planar maps
    Groupe de travail de combinatoire énumérative et algébraic, LaBRI, Université de Bordeaux, France, March 2019.
  • Enumerating permutations sortable by two stacks in series, two stacks in parallel and a double ended queue
    Seminaire SPACE Tours, IDP, Université de Tours, France, October 2018.
  • The generating function of planar Eulerian orientations
    Mathematical physics seminar, University of Melbourne, Australia, October 2018.
  • Enumerating planar Eulerian orientations
    Discrete mathematics research group, Monash university, Melbourne, Australia, November 2017.
  • Two enumerative algorithms
    Mathematical physics seminar, University of Melbourne, Australia, October 2017.
  • Enumerating Planar maps qeighted by their Tutte polynomial
    Tutte centenary event, Monash university, Melbourne, Australia, September 2017.
  • Enumeration in Thompson’s group F
    Groupe de travail de combinatoire énumérative et algébraic, LaBRI, Université de Bordeaux, June 2017.
  • Enumerating 1324-avoiding permutations
    Mathematical physics seminar, University of Melbourne, Australia, November 2016.