Post-Doc at LaBRI, Université de Bordeaux and IDP, Université de Tours, France.

Research teams : SPACE (IDP), CEA (LaBRI).

**Contact**

Email : **Adresse postale**

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

**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

**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)**C****ounting 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.