- Enumeration of combinatorial maps
- Mostly I work on constellations, but I am also interested in other maps. Usually I use algebraic methods (characters, fonctional equations) on exact counting, but I am also very interested in bijections and asymptotics.
- Random aspects of combinatorial objects
- Mostly those related to maps that I have studied. I am interested mainly in their limit shape and statistics, but also random generation.
- Combinatorial interpretation of characters of symmetric group
- This is derived from my interests in maps. I am interested in the interaction between characters, tableaux and maps.
- Some other combinatorial models
- I have been interested also in sandpile model (not to confuse with abelian sandpile model, though they interest me too), mainly in enumeration and generation.
- Verification of conjectures with volunteer computing
- Mostly by exhaustive search, so I have to ask volunteers from all over the world to do it. With their help, I have verified quite a few conjectures on unpreceded size (small comparing to infinity though).
List of publications
Publications on journals and international conferences
Subcritical random hypergraphs, high-order components, and hypertrees
With Oliver Cooley, Nicola Del Giudice and Mihyun Kang
Submitted. arXiv version at 1810.08107.
Extended abstract accepted by Analytic Algorithmics and Combinatorics 2019 (ANALCO 2019)
Fighting fish and two-stack sortable permutations
In preparation. arXiv version 1711.05713
Extended abstract accepted by The 30th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2018)
Enumeration of cubic multigraphs on orientable surfaces
With Mihyun Kang, Michael Moßhammer, Philipp Sprüssel
Electronic Journal of Combinatorics, Volume 25, Issue 1, 2018, Paper #P1.30.
Extended abstract accepted by European Conference on Combinatorics, Graph Theory and Applications 2015 (EuroComb 2015)
Planar triangulations, bridgeless planar maps and Tamari intervals
European Journal of Combinatorics, Volume 70, 2018. arXiv version at 1611.07922.
A trinity of duality: Non-separable planar maps, β-(1,0) trees and synchronized intervals
Advances in Applied Mathematics, Volume 95, 2018. arXiv version at 1703.02774.
Parallel Tree Search in Volunteer Computing: a Case Study
With Uwe Beckert
Journal of Grid Computing, 2017. Volume yet to be assigned. Open access.
Generating functions of bipartite maps on orientable surfaces
With Guillaume Chapuy
Electronic Journal of Combinatorics, Volume 23, Issue 3, 2016, Paper #P3.31
Extended abstract accepted by The 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
arXiv version at 1502.06239
The enumeration of generalized Tamari intervals
With Louis-François Préville-Ratelle
European Journal of Combinatorics, Volume 61, 2017.
Extended abstract accepted by The 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), under the title From generalized Tamari intervals to non-separable planar maps (extended abstract)
Bijective proofs of character evaluations using trace forest of the jeu de taquin
Séminaire Lotharingien de Combinatoire, Volume 72, 2015, Pages B72e
arXiv version at 1403.5679
A Recursive Structure of Sand Pile Model and Its Applications
With Roberto Mantaci
Pure Mathematics and Applications, Volume 25, Issue 1, Pages 63-78
A sample implementation of the constant amortized time algorithm in the article can be found here.
A generalization of the quadrangulation relation to constellations and hypermaps
Journal of Combinatorial Theory, Series A (JCTA), Volume 127, September 2014, Pages 1-21
Extended abstract accepted by The 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
arXiv version at 1311.6991
On the Hyperbolicity of Small-World Networks and Tree-Like Graphs
With Wei Chen, Guangda Hu and Michael W. Mahoney
Internet Mathematics, Volume 9, 2013, Pages 434-491
Also accepted as conference paper by The 23rd International Symposium on Algorithms and Computation (ISAAC 2012)
arXiv version at 1201.1717
How to scatter a secret?
With Eric Brier and David Naccache
Cryptologia, Volume 36 Issue 1, 2012
Manuscripts, informal publications, technical reports
The Steep-Bounce Zeta Map in Parabolic Cataland
With Cesar Ceballos and Henri Mühle
A partial order on Motzkin paths
arXiv 1801.04809, 2018
New Computational Result on Harmonious Trees
arXiv 1106.3490, 2011
A Computational Approach to the Graceful Tree Conjecture
arXiv 1003.3045, 2010