- (with Christian Krattenthaler) Cyclic sieving phenomena for
trees and tree-rooted maps.
- (with Hadrien Notarantonio)
The 3-state Potts model on planar triangulations: explicit algebraic solution.
A Maple session that accompanies the paper, together with two collections of files where intermediate results are saved.
- (with Ariane Carrance and
Baptiste Louf) The Ising model on cubic maps: arbitrary genus.
A Maple session that accompanies the paper. SageMath companion file: ipynb, html
- (with Andrew Elvey Price)
Refined enumeration of planar Eulerian orientations.
A Maple session that accompanies the paper.
2025
2024
- (with Jean-Luc Baril,
Sergey Kirgizov and
Mehdi Naima) The ascent lattice of Dyck
paths,
Elec. J. Combinatorics 32 no. 2 (2025).
A Maple session that accompanies the paper.
journal
2023
- (with Frédéric Chapoton) Intervals in the greedy Tamari posets, Combinatorial Theory Vol. 4, Issue 1, paper no.5
2022
- (with Andrey Elvey
Price,
Sandro Franceschi,
Charlotte Hardouin
and Kilian
Raschel)
On the stationary distribution of reflected Brownian motion in a wedge: differential properties,
substantially revised version of the 2021 preprint.
Electron. J. Probab. 30 (2025) 1-68.
A Maple session that accompanies the paper.
journal
2021
- Enumeration of three-quadrant walks via invariants: some diagonally symmetric models,
Canad. J. Math., 75 (5) 2023
There are six accompanying Maple sessions, one for each model that is solved in the paper: Kreweras model, reverse Kreweras model, double Kreweras model, a D-algebraic model, simple walks, diagonal walks.
journal
- (with Michael Wallner)
Walks avoiding a quadrant and the reflection principle,
Europ. J. Combinatorics, 119 (2024).
This is the full version of the conference paper "More models of walks avoiding a quadrant" from 2020.
Some accompanying Maple sessions: two for standard king walks (part 1 and part 2), two others when one allows steps between (0,-1) and (-1,0) (part 1 and part 2). In each case, one first establishes a system of four polynomial equations (first case, second case) and then derives four individual polynomials equations (first case; for the second case, this is done in the Maple session "Part2" given above). In the first case the four equations are in fact guessed from their first 2000 coefficients, given in these files: series R0, series R1, series B1, series B2.
journal
2020
- (with Michael
Wallner)
More models of walks avoiding a quadrant (extended abstract). Proceedings of Analysis of Algorithms 2020, LIPICS 150, p. 8:1--8:14.
2019
- (with Éric Fusy and Kilian Raschel) Plane bipolar orientations and quadrant walks, Séminaire Lotharingien de Combinatoire, 81B, article [B81l] (63 pages)
- (with Andrew Elvey Price and Paul Zinn-Justin) Eulerian orientations and the six-vertex model on planar maps, Extended abstract accepted to FPSAC 2019 (Formal Power Series and Algebraic Combinatorics). Séminaire Lotharingien de Combinatoire 82B, article [82B.70] (12 pages)
2018
- (with Alin Bostan
and Steve Melczer)
Counting walks with large steps in an orthant,
J. Europ. Math. Soc.
23 (7) 2021, pp. 2221–2297Here are some accompanying Maple sessions. First, a program that determines whether the orbit of a 2D model is finite (Section 3.2). Then, some files and sessions related to Section 8: the list of the 12883 non-Hadamard models, determination of the corresponding excursion exponent, and finally the asymptotic calculations of Section 9.
journal
- (with Andrew Elvey Price) The generating function of planar Eulerian orientations, J. Combin. Theory Ser. A. 172 (2020) 105183.
2017
-
(avec Olivier Bernardi
et Kilian Raschel)
Counting quadrant walks via Tutte's invariant method.
Full version of the FPSAC 2016 extended abstract (see below in 2015).
Combinatorial Theory, 1, paper # 3.
The main accompanying Maple session is this one. It points to four other sessions, for the calculation of invariants, of decoupling functions, for proving that no such function exists, and solving the algebraic models.
journal
2016
- (avec Riccardo Biagioli, Frédéric Jouhet et Philippe Nadeau) Length enumeration of fully commutative elements in finite and affine Coxeter groups, J. Algebra, 513 (2018) 466-515.
-
(avec Nicolas Bonichon, Paul Dorbec
et Claire Pennarun)
On the number of planar Eulerian orientations,
Europ. J. Combin. 65 (2017) 59-91.
The accompanying Maple session, and a C++ program that computes the number of Eulerian orientations of small size.
journal
- (avec Michèle Soria et Robert Sedgewick) Special issue of Algorithmica with a selection of papers presented at the conference Analysis of Algorithms 2014.
2015
- (avec Olivier Bernardi et Kilian Raschel) Counting quadrant walks via Tutte's invariant method (extended abstract), ArXiv:1511.04298. Extended abstract of a talk at the conference FPSAC 2016. The full version appears above (2017).
-
Plane lattice walks avoiding a quadrant,
J. Combin. Theory Ser. A,
144 (2016) 37-79.
Special issue "Fifty years of the Journal of
Combinatorial Theory".
The accompanying Maple sessions: one for the square lattice, the other for the diagonal square lattice.
journal
-
(avec Olivier
Bernardi)
Counting coloured planar maps: differential
equations, Comm. Math. Phys. 354 no. 1
(2017) 31–84.
The accompanying Maple sessions: one for general planar maps, the other for triangulations.
journal
-
An elementary solution of Gessel's walks in the quadrant,
Adv. Math. 303 (2016) 1171-1189.
The accompanying Maple session.
journal
2014
-
(avec Alin Bostan, Manuel
Kauers, Steve
Melczer)
On 3-dimensional lattice walks confined to the positive octant,
Annals of Comb. 20(4),
661-704 (2016)
Supplementary material available on Manuel Kauers' webpage.
journal
2013
- (avec Michael Albert) Permutations sortable by two stacks in parallel and quarter plane walks, Europ. J. Combin. 43 , January 2015, p. 131–164
- (avec Markus Lohrey, Sebastian Maneth, Eric Noeth) XML Compression via DAGs, Theory of Computing Systems 57, no. 4 (2015) 1322–1371.
- (avec Julien Courtiel) Spanning forests in regular planar maps, J. Combin. Theory Ser. A 135 October 2015, 1–59
- (avec Kerstin Weller)Asymptotic properties of some minor-closed classes of graphs, arXiv:1303.3836, 2013. Combinatorics, Probability and Computing 23 (5) pp. 749-795 (2014).
2012
- (avec Nick Beaton, Jan de Gier, Hugo Duminil-Copin et Tony Guttmann) The critical fugacity for surface adsorption of self-avoiding walks on the honeycomb lattice is 1+sqrt(2), Communications in Mathematical Physics, 326 (3) pp 727-754 (2014).
- (avec Guillaume Chapuy) The vertical profile of embedded trees, Electronic J. Combinatorics , 19 no. 3, Paper P46, 2012.
- (avec Guillaume Chapuy et Louis-François Préville-Ratelle) The representation of the symmetric group on m-Tamari intervals, Adv. Math. 247 (2013) 309–342. Subsumes the other paper by the same authors, just below.
2011, l'année des tamaris
- (avec Guillaume
Chapuy et Louis-François
Préville-Ratelle)
Tamari lattices and parking functions: proof of a conjecture of
F. Bergeron
- (avec Éric Fusy and Louis-François Préville Ratelle) The number of intervals in the m-Tamari lattices, Electronic J. Combinatorics , 18 no. 2, paper R31, 26 pp.
- On the importance sampling of self-avoiding walks, Combin. Probab. Comput. 23 (5), pp. 725-748 (2014).
2010
- (avec Andrei Asinowski, Gill Barequet, Toufik Mansour, Ron Pinter) Orders induced by segments in floorplan partitions and (2-14-3,3-41-2)-avoiding permutations, Electronic J. Combinatorics 20 no. 2 (2013) P35.
- (avec Axel Bacher) Weakly directed self-avoiding walks, J. Combin. Theory Ser. A 118 no.~8 (2011) 2365--2391. Arxiv:.
- Counting permutations with no long monotone subsequence via generating trees and the kernel method, J. Alg. Combin. 33 no.~4 (2011) 571--608.
-
Counting planar maps, coloured or uncoloured, Invited survey for the 23rd
Bristish Combinatorial Conference, Exeter, July 2011.
London Math. Soc. Lecture Note Ser.
392 (2011) 1--50. R. Chapman ed.
2009
-
(avec Olivier Bernardi)
Counting colored planar maps: algebraicity results,
J. Combin. Theory
ser. B 101 no. 5 (2011) 315-377.
Two Maple sessions accompany this paper: one for general planar maps, the other for triangulations. These two sessions, exported in html format, can be found here and here.
journal
- The expected number of inversions after n adjacent transpositions, Discrete Math. Theoret. Comput. Sci. 12 no.2 (2010) 65-88.
- (avec James Propp and Julian West) Perfect matchings for the three-term Gale-Robinson sequences, Electronic J. Combinatorics , 16 no. 1, R125.
- (avec Anders Claesson, Mark Dukes, Sergey Kitaev) (2+2)-Free posets, ascent sequences and pattern avoiding permutations, J. Combin. Theory Ser. A 117 no. 7 (2010) 884-909.
2008
- (avec Richard Brak)
Exactly solved models of polyominoes and polygons,
Chapter 3 of Polygons, Polyominoes and Polycubes,
Lecture Notes in Physics, Volume 775, pp. 43-78,
Springer Berlin / Heidelberg 2009.
- (avec Marni Mishna)
Walks with small steps in the quarter plane,
Contemp. Math. 520 (2010) 1--40.
- (avec Nicolas Bonichon et Éric Fusy) Baxter permutations and plane bipolar orientations, Séminaire Lotharingien de Combinatoire 61A , article [B61Ah] (29 pages)
- Families of prudent self-avoiding walks, J. Combin. Theory Ser. A 117 no. 3 (2010) 313-344.
- A property of dominance of partitions (note).
2007
- (with
Yann Ponty)
Culminating paths,
Discrete
Math and Theoretical Computer Science, 10 no. 2 (2008) 125-152.
The associated random generators can be found
here.
- (with Svante Linusson and Eran Nevo) On the independence complex of square grids, J. Alg. Combinatorics, 27 (2008) 423-450.
- Discrete excursions, Séminaire Lotharingien de Combinatoire, vol. 57, 2008.
2006
- (avec Steven Butler) Forest-like permutations, Ann. Comb. 11 (2007) 335-354.
- Three osculating walkers, Journal of Physics: Conference Series 42 (2006) 35-46.
- (avec Svante Janson) The density of the ISE and local limit laws for embedded trees, Annals Applied Proba. 16 No. 3 (2006) 1597-1632.
- (avec A. Jehanne) Polynomial equations with one catalytic variable, algebraic series and map enumeration, J. Combin. Theory Ser. B 96 (2006) 623--672.
- Limit laws for embedded trees. Applications to the integrated superBrownian excursion, Random Structures and Algorithms 29 Number 4, (2006) 475--523.
- Rational and algebraic series in combinatorial enumeration, invited paper for the International Congress of Mathematicians 2006. Proceedings of the ICM. Session lectures, vol. III, pp. 789--826.
2005
- (Avec A.J. Guttmann and I. Jensen) Self-avoiding walks crossing a square<, J. Phys. A: Math. Gen. 38 (2005) 9159-9181.
- Walks in the quarter plane: Kreweras' algebraic model, Annals of Applied Probability, 15 No. 2 (2005) 1451-1491. A (minor) erratum on this paper.
- (avec G. Xin) On partitions avoiding 3-crossings, Séminaire Lotharingien de Combinatoire, Vol. 54, paper B54e (21 pp.)
- (avec Einar Steingrimsson) Decreasing subsequences in permutations and Wilf equivalence for involutions, J. of Algebraic Combinatorics, 22 No. 4 (2005) 383 - 409
- Algebraic generating functions in enumerative combinatorics, and context-free languages, invited paper for STACS 2005, Lect. Notes Comput. Sci. 3404 (2005) 18--35.
2004
-
Nada!
2003
- (avec Marko Petkovsek) Walks confined in a quadrant are not always D-finite, Theoret. Comput. Sci. 307 (2003) 257-276.
- Four classes of pattern-avoiding permutations under one roof: generating trees with two labels, Electronic J. Combinatorics 9 no. 2 (2003) R19.
- (avec A. Rechnitzer) The site-perimeter of bargraphs, Adv. in Applied Math 31 (2003) 86-112.
2002
- Counting walks in the quarter plane, in Mathematics and Computer Science: Algorithms, trees, combinatorics and probabilities, Trends in Mathematics, Birkhauser, 2002, pp. 49--67.
- Walks in the quarter plane: a functional equation approach, FPSAC 2002, Melbourne.
- (avec Gilles Schaeffer) The degree distribution of bipartite planar maps: applications to the Ising model, math.CO/0211070.
- (avec Gilles Schaeffer) Walks on the slit plane, Probab. Theory Relat. Fields 124 no.3 (2002) 305-344.
- (avec Cyril Banderier, Alain Denise, Philippe Flajolet, Danièle Gardy, Dominique Gouyou-Beauchamps) Generating functions for generating trees, Discrete Math. 246 no.1-3 (2002) 29--55.
- (avec
Andrew Rechnitzer)
Lattice animals and heaps
of dimers, Discrete Math. 258 (2002) 235-274.
Some pictures of animals of fixed size drawn uniformly at random: directed animals, stacked directed animals, and multi-directed animals. Another (much bigger) multi-directed animal, generated by Axel Bacher following the algorithm described in his paper Directed and multi-directed animals on the king's lattice.
2001
- Walks on the slit plane: other approaches, Advances in Applied Math 27 No.2-3 (2001) 243-288.
- On (some) functional equations arising in enumerative combinatorics, extended abstract for FPSAC 2001.
- (avec I. Dutour et G. Melançon) Random generation of dags for graph drawing, Electronic Notes in Discrete Mathematics 10, (November 2001). Proceedings of Comb01, Euroconference on Combinatorics, Graph Theory and Applications. CRM, Bellaterra, Barcelona, Spain, 12 - 15 September 2001. Edited by Jaroslav Nesetril, Marc Noy and Oriol Serra
2000
- (avec Gilles Schaeffer) Counting paths on the slit plane (extended abstract of the first paper), in Mathematics and Computer Science: Algorithms, trees, combinatorics and probabilities, Trends in Mathematics, Birkhauser, 2000.
- Sorted and/or sortable permutations, Discrete Math. 225 (2000) 25--50.
- (avec Gilles Schaeffer) Enumeration of planar constellations, Advances in Applied Math. 24 (2000) 337-368.
- (avec Marko Petkovsek) Linear recurrences with constant coefficients: the multivariate case, Discrete Math. 225 (2000) 51--75.
1999
- (avec Kimmo Eriksson) A refinement of the Lecture Hall Theorem, J. Combin. Theory Ser. A. 86 (1999) 63-84.
- (avec A. J. Guttmann, W. P. Orrick, A. Rechnitzer) Inversion relations, reciprocity and polyominoes, Annals of Combinatorics 3 No.2-4 (1999) 223-249.
1998
- Multi-statistic enumeration of two-stack sortable permutations, Electronic J. Combinatorics 5 (1998) R21.
- New enumerative results on two-dimensional directed animals , Discrete Math. 180 (1998) 73-106.
1997
- (avec Kimmo Eriksson) Lecture Hall Partitions , The Ramanujan Journal 1 No.1 (1997) 101-111.
- (avec Kimmo Eriksson) Lecture Hall Partitions 2, The Ramanujan Journal 1 No.2 (1997) 165-185.
- (avec A. J. Guttmann) Enumeration of three-dimensional convex polygons (25 pages, PostScript compressé, 107K), Annals of Combinatorics 1 No.1 (1997) 27-53.
- (avec A. J. Guttmann) Three-dimensional convex polygons, Phys. Rev. E 55 (1997) R6323-6326.
1996
- (avec Andrew Conway) Enumeration of directed animals on an infinite family of lattices , J. Phys. A: Math. Gen. 29 (1996) 3357-3365.
- A method for the enumeration of various classes of column-convex polygons , Discrete Math. 154 (1996) 1-25.
- Percolation models and animals , European J. Combin. 17 (1996) 343-369.
- Habilitation (89 pages, Postscript compressé, 256K)
1995
- (avec Jean-Marc Fédou) The generating function of convex polyominoes : the resolution of a q-differential system, Discrete Math. 137 (1995) 53-75.
- (avec Laurent Habsieger) Sur les matrices à signes alternants, Discrete Math. 139 (1995) 57-72.
- (avec François Bergeron et Serge Dulucq) Standard paths in the composition poset, Ann. Sci. Math. Québec 19 (1995) 139-151.
- (avec Jean-Paul Allouche) On the conjectures of Rauzy and Shallit for infinite words Commentationes Math. Univ. Carolinae 36 (1995), 705-712.
1994
- Codage des polyominos convexes et équations pour l'énumération suivant l'aire, Discrete Appl. Math. 48 (1994) 21-43.
- Polyominoes and polygons , ``Jerusalem Combinatorics '93'' (H. Barcelo, G. Kalai eds.), Contemporary Mathematics (AMS) 178 (1994) 55-70.
- (avec Jean-Paul Allouche ) Canonical positions for the factors in the paperfolding sequences , Theoret. Comput. Science 129 (1994) 263-278.
- (avec Jean-Paul Allouche) Facteurs des suites de Rudin-Shapiro généralisées , Journées Montoises d'Informatique Théorique, Bulletin of the Belgian Math. Society 1 (1994) 145-164.
1993
- q-Énumération de polyominos convexes, J. Combin. Theory Ser. A 64 (1993) 265-288.
1992
- The number of minimal word chains computing the Thue-Morse word, Inform. Process. Lett. 44 (1992) 57-64.
- Convex polyominoes and heaps of segments, J. Phys. A : Math. Gen. 25 (1992) 1925-1934.
- Convex polyominoes and algebraic languages, J. Phys. A : Math. Gen. 25 (1992) 1935-1944.
- Une bijection entre les polyominos convexes dirigés et les mots de Dyck bilatères, Inf. Th. et Appl. 26 (1992) 205-219.
- (avec Xavier Viennot) Empilements de segments et q-énumération de polyominos convexes dirigés, J. Combin. Theory Ser. A 60 (1992) 196-224.