Research
Research interests
- Combinatorial maps
- Enumeration (exact and asymptotic) via various methods, and also bijections with other combinatorial objects, especially Tamari intervals.
- Random aspects of combinatorial objects
- Mostly those related to maps that I have studied, but also some tree-based structures. 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
-
Bijections between planar maps and planar linear normal λ-terms with connectivity condition
Advances in Applied Mathematics, Volume 148, Article 102532, 2023. arXiv 2202.03542, 2022.
Extended abstract accepted by The 35th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2023).
-
Parabolic Tamari Lattices in Linear Type B
With Henri Mühle and Jean-Christophe Novelli.
arXiv 2112.13400, 2021
Extended abstract accepted by The 34th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2022).
-
Efficient recurrence for the enumeration of permutations with fixed pinnacle set
Discrete Mathematics & Theorectical Computer Science, Volume 24, Issue 1, #8, 2022. arXiv 2106.09147, 2021
-
A character approach to directed genus distribution of graphs: the bipartite single-black-vertex case
With Yichao Chen.
Discrete Mathematics, Volume 345, Issue 6, 112833, 2022. arXiv 2005.11703, 2020
-
A Consecutive Lehmer Code for Parabolic Quotients of the Symmetric Group
With Henri Mühle and Jean-Christophe Novelli.
Electronic Journal of Combinatorics, Volume 28, Issue 3, P3.53, 2021. arXiv 2009.05342, 2020
-
Bijective link between Chapoton's new intervals and bipartite planar maps
European Journal of Combinatorics, Volume 97, 2021. arXiv full version 2001.04723.
Extended abstract accepted by The 32th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2020).
-
Phase transitions from $\exp(n^{1/2})$ to $\exp(n^{2/3})$ in the asymptotics of banded plane partitions
With Hsien-Kuei Hwang and Mihyun Kang
Journal of Combinatorial Theory Series A, Volume 178, 2021. arXiv version at 2004.08901.
-
Compacted binary trees admit a stretched exponential
With Andrew Elvey Price and Michael Wallner
Journal of Combinatorial Theory Series A, Volume 177, 2021. arXiv version at 1908.11181.
-
Asymptotics of Minimal Deterministic Finite Automata Recognizing a Finite Binary Language
With Andrew Elvey Price and Michael Wallner
Conference paper accepted by The 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA2020). Full text.
-
Subcritical random hypergraphs, high-order components, and hypertrees
With Oliver Cooley, Nicola Del Giudice and Mihyun Kang
SIAM Journal on Discrete Mathematics, Volume 34, Issue 4, 2020.
arXiv version at 1810.08107.
Extended abstract accepted by Analytic Algorithmics and Combinatorics 2019 (ANALCO 2019)
-
The Steep-Bounce Zeta Map in Parabolic Cataland
With Cesar Ceballos and Henri Mühle
Journal of Combinatorial Theory Series A, Volume 172, 2020. arXiv version at 1903.08515.
Extended abstract accepted by The 31th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2019).
-
Absolute root separation
With Yann Bugeaud, Andrej Dujella, Tomislav Pejković and Bruno Salvy
Experimental Mathematics, 2020. arXiv version at 1907.01232.
-
A partial order on Motzkin paths
Discrete Mathematics, Volume 343, Issue 5, 2020. arXiv version at 1801.04809.
-
Fighting fish and two-stack sortable permutations
arXiv full 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)
arXiv 1511.05937
-
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
-
Bijective proof of a conjecture on unit interval posets
arXiv 2212.13040, 2022
-
Searching on the boundary of abundance for odd weird numbers
arXiv 2207.12906, 2022
-
New Computational Result on Harmonious Trees
arXiv 1106.3490, 2011
-
A Computational Approach to the Graceful Tree Conjecture
arXiv 1003.3045, 2010
Participation in research projects
-
ANR 3DMaps (ANR-20-CE48-0018, Adrian Tanasa), 2021 -- 2025
-
ANR LambdaComb (ANR-21-CE48-0017, Noam Zeilberger), 2021 -- 2025
-
ANR PAGCAP (ANR-21-CE48-0020, Viviane Pons, Cesar Ceballos), 2022 -- 2026
-
ANR IsOMA (Marie Albenque), in administrative process