## Articles

### Preprints

- Combinatorial foundations for geometric realizations of subword complexes of Coxeter groups
- J.-P. Labbé, July 2020

### Publications

#### Quantum Theory

- An effective solution to convex 1-body N-representability
F. Castillo, J.-P. Labbé, J. Liebert, A. Padrol, E. Philippe, C. Schilling
*Ann. Henri Poincaré*, (2023), in print. - Foundation of one-particle reduced density matrix functional theory for excited states
J Liebert, F. Castillo, J.-P. Labbé, C. Schilling
*J. Chem. Theory Comput.*,**18**, (2022) no. 1, 124-140.

#### Discrete Geometry

- Congruence Normality of Simplicial Hyperplane Arrangements via Oriented Matroids
M. Cuntz, S. Elia, J.-P. Labbé,
*Ann. Comb.*,**26**, (2022) no. 1, 1-85. - Combinatorial inscribability obstructions for higher-dimensional polytopes
J. Doolittle, J.-P. Labbé, C. Lange, R. Sinn, J. Spreer, G.M. Ziegler,
*Mathematika*,**66**, (2020), no. 4, 927-953. - Area difference bounds for dissections of a square into an odd number of triangles
J.-P. Labbé, G. Rote, G.M. Ziegler,
*Exp. Math.*,**29**, (2020), no. 3, 253-275. - Fan Realizations of Type A Subword Complexes and Multi-associahedra of Rank 3
N. Bergeron, C. Ceballos, and J.-P. Labbé,
*Discrete Comput. Geom.*,**54**(2015), no. 1, 195-231.

#### Combinatorics of Simplicial Complexes

- Bounds for entries of γ-vectors of flag simplicial spheres
J.-P. Labbé, E. Nevo,
*SIAM J. Discrete Math.*,**31**, (2017), no. 3, 2064-2078. - Hirsch polytopes with exponentially long combinatorial segments
J.-P. Labbé, T. Manneville, and F. Santos,
*Math. Program.*,**165**(2017), no. 2, 663–688.

#### Geometric Group Theory / Coxeter Groups

- Limit directions for Lorentzian Coxeter systems
H. Chen and J.-P. Labbé,
*Groups Geom. Dyn.*,**11**, (2017), 469-498. - On inversion sets and the weak order in Coxeter groups
C. Hohlweg and J.-P. Labbé,
*European J. Combin.*,**55**, (2016), 1-19. - Lorentzian Coxeter groups and Boyd-Maxwell ball packings
H. Chen and J.-P. Labbé,
*Geom. Dedic.*,**74**(2015), no. 1, 43-73. - Asymptotical behaviour of roots of infinite Coxeter groups
C. Hohlweg, J.-P. Labbé, and V. Ripoll,
*Canad. J. Math.***66**(2014), no. 2, 323-353.

#### Geometric Structures in Cluster Algebras

- Cluster Algebras of Type D4, Tropical Planes, and the Positive Tropical Grassmannian
S.B. Brodsky, C. Ceballos and J.-P. Labbé,
*Beitr. Algebra Geom.*,**58**, (2017), no. 1, 25-46. We use the combinatorics of pseudo-triangulations of the octogon to characterize the combinatorial types of generic tropical planes in the tropical projective space of dimension 5.

- Subword complexes, cluster complexes, and generalized multiassociahedra
C. Ceballos, J.-P. Labbé and C. Stump,
*J. Algebraic Comb.***39**(2014), no. 1, 17-51. We provide an interpretation of finite cluster complexes and multi-triangulations using the combinatorics of subword complexes of Coxeter groups.

#### Combinatorics

- Cambrian acyclic domains: counting c-singletons
J.-P. Labbé, C. Lange,
*Order*,**37**, (2020), no. 3, 571-603. We provide lower and upper bounds for the number of common vertices of associahedra and permutahedra stemming from Hohlweg--Lange--Thomas' construction.

- Counting Types of Runs in Classes of Arborescent Words
J.-P. Labbé and G. Labelle,
*Open Journal of Discrete Mathematics***3**(2013), no. 1, 7-15. We use species of structures to generalize the notion of*runs*in cointosses to general runs in arborescent words and obtain the generating series for various types of runs. - Combinatorial variations on Cantor's diagonal
S. Brlek, J.-P. Labbé and M. Mendès France,
*J. Comb. Theory, Ser. A***119**(2012), no. 3, 655-667. We use group actions in order to facilitate the enumeration of tableaux which are finite analogues of Cantor's famous diagonal argument.

#### Unpublished Preprints

- A Perron theorem for matrices with negative entries and applications to Coxeter groups
- J.-P. Labbé, S. Labbé, November 2015

### Conferences

It is possible to view the videos on my videos page.

- Universal Oriented Matroids for Subword Complexes of Coxeter Groups (Poster), FPSAC 2020, 8th July 2020
- Combinatorics and geometry of polyhedra in Sage, Global Virtual SageDays 109, 27th May 2020
- Convex Geometry of Subword Complexes, Nonlinear Algebra Seminar Online, Max Planck Institute Leipzig, 19th March 2020
- Experimental Coxeter Group Theory, Sage Days, Institute for Mathematics and its Applications, 23rd August 2017

## Theses

- Convex Geometry of Subword Complexes of Coxeter Groups, Habilitationsschrift, Freie Universität Berlin, 2020
- Polyhedral Combinatorics of Coxeter Groups, Dissertation, Freie Universität Berlin, 2013
- Combinatorial approach to clusters using sortable elements of Coxeter groups [in French], Mémoire de maîtrise en mathématiques, UQAM, 2010, 105 p.
- Soyons des designers! [in French], Projet de fin d'études, Université Laval, 2008, 37 p.

## Research visits

- Gradignan (France), February-March (2 weeks) 2011, with S. Brlek and M. Mendès France
- LaCIM-UQÀM, Montréal (Québec), June-July (2 weeks) 2011, with C. Hohlweg
- LaCIM-UQÀM, Montréal (Québec), August (2 weeks) 2012, with C. Hohlweg
- Jussieu/Polytechnique, Paris (France), February-March (2 weeks) 2013, with V. Pilaud and C. Lange
- Université de Paris Diderot-Paris 7, LIAFA, June (1 week) 2014, with S. Labbé
- Oberwolfach - Geometric and Algebraic Combinatorics, February 2015
- Universitad de Cantabria, Santander, Spain, February-March 2015, with F. Santos
- Universitad de Cantabria, Santander, Spain, September-October 2015, with F. Santos
- IMA, Minneapolis, USA, April 2018
- Research in Pairs, Oberwolfach, Germany, May 2019

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