CNRS researcher at IDP, Université de Tours, France.

Research team : SPACE.

**Contact**

Email : **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

**Selected Problems in Enumerative Combinatorics**

PhD Thesis (2018), Supervised by Tony Guttmann.**Geodesics in Cayley Graphs**Masters thesis (2014), Supervised by Lawrence Reeves.

### 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.