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CNRS researcher at IDP, Université de Tours, France.
Research team : SPACE.

Contact
Email : andrew.elvey-price@cnrs.fr
Postal Adress
Andrew Elvey Price
Institut Denis Poisson, Université de Tours, Parc grandmont
37200 Tours, France

Research

I am a CNRS researcher in the SPACE team at Institut Denis Poisson, université de 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. Here is a list of all OEIS sequences with atleast 15 terms that may be Stieltjes moment sequences (up to A369485, as of 25/01/2024).

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

  • The six vertex model on random planar maps revisited
    With Paul Zinn-Justin
    Journal of Combinatorial Theory A 196 (2023): 105739 (submitted before the replacement journal Combinatorial theory was created) arXiv:2007.07928
  • A Cayley graph for F_2×F_2 which is not minimally almost convex
    International Journal of Algebra and Computation 32.01 (2022) arXiv:1611.00101
  • Pattern-Avoiding Ascent Sequences of Length 3
    With Andrew R Conway, Miles Conway and Tony Guttmann
    Electronic Journal of combinatorics 29.4 (2022): P4.25 arXiv:2111.01279
  • Bijections between walks inside a triangular domain and Motzkin paths of bounded amplitude
    With Julien Courtiel and Irène Marcovici
    Electronic Journal of combinatorics 28.2 (2021): P2.6 arXiv:2007.08868
  • Asymptotics of 3-stack-sortable permutations
    With Colin Defant and Tony Guttmann
    Electronic Journal of combinatorics 28.2 (2021): P2.49 arXiv:2009.10439
  • Stieltjes moments sequences for pattern-avoiding permutations
    With Alin Bostan, Tony Guttmann and Jean-Marie Maillard
    Electronic Journal of combinatorics 27.4 (2020): P4.20 arXiv:2001.00393
  • Phylogenetic trees, augmented perfect matchings and a Thron-type continued fraction (T-fraction) for the Ward polynomials
    With Alan Sokal
    Electronic Journal of combinatorics 27.4 (2020): P4.6 arXiv:2001.01468
  • Compacted binary trees admit a stretched exponential
    With Wenjie Fang and Michael Wallner
    Journal of Combinatorial theory A 177 (2020): 105306 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 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

  • Enumeration of walks with small steps avoiding a quadrant
    FPSAC 2022. Proceedings of the 34nd conference on Formal Power Series and Algebraic Combinatorics. pdf
  • 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. pdf
  • Counting lattice walks by winding angle
    FPSAC 2020. Proceedings of the 32nd conference on Formal Power Series and Algebraic Combinatorics. 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. pdf

Preprints and Submissions

  • Enumeration of three quadrant walks with small steps and walks on other M-quadrant cones
    arXiv:2204.06847 (2022)
  • The stationary distribution of reflected Brownian motion in a wedge: differential properties
    With Mireille Bousquet-Mélou, Sandro Franceschi, Charlotte Hardouin and Kilian Raschel
    arXiv:2101.01562 (2021)
  • Permutations sortable by deques and two stacks in parallel share the same growth rate
    arXiv:1912.00056 (2019)

Articles in preparation

  • 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
  • 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.