Lionel Pournin
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Preprints

[–]
Flat simplices and kissing polytopes
with A. Deza
Preprint (2026) - [arXiv]
[–]
Flip-graphs of non-orientable filling surfaces
with P. Panda and H. Parlier
Preprint (2025) - [arXiv]
[–]
Geometry of sparsity-inducing norms
with J.-P. Chancelier, M. de Lara, and A. Deza
Preprint (2025) - [arXiv]
[–]
Deep sections of the hypercube
Preprint (2024) - [arXiv]
[–]
Strong convexity in flip-graphs
with Z. Wang
Preprint (2021) - [arXiv]

Journal articles

The expansion of half-integral polytopes
with J. Cardinal
Michigan Mathematical Journal, to appear - [arXiv]
Kissing polytopes in dimension 3
with A. Deza and Z. Liu
Experimental Mathematics, to appear - [arXiv]
Small kissing polytopes
with A. Deza and Z. Liu
Vietnam Journal of Mathematics 53(4), 901–913 (2025) - [arXiv/supplementary material]
Many equiprojective polytopes
with T. Buffière
Discrete & Computational Geometry 74(2) 337–357 (2025) - [arXiv]
Counting geodesics between surface triangulations
with H. Parlier
Mathematical Proceedings of the Cambridge Philosophical Society 178(1), 45–63 (2025) - [arXiv]
Kissing polytopes
with A. Deza, S. Onn, and S. Pokutta
SIAM Journal on Discrete Mathematics 38(4), 2643–2664 (2024) - [arXiv]
Local extrema for hypercube sections
Journal d'Analyse Mathématique 152(2), 557–594 (2024) - [arXiv/corrigendum]
The rotation distance of brooms
with J. Cardinal and M. Valencia-Pabon
European Journal of Combinatorics 118, 103877 (2024) - [arXiv]
The complexity of geometric scaling
with A. Deza and S. Pokutta
Operations Research Letters 52, 107057 (2024) - [arXiv]
Shallow sections of the hypercube
Israel Journal of Mathematics 255(2), 685–704 (2023) - [arXiv]
Diameter estimates for graph associahedra
with J. Cardinal and M. Valencia-Pabon
Annals of Combinatorics 26(4), 873–902 (2022) - [arXiv]
Primitive point packing
with A. Deza
Mathematika 68(3), 979–1007 (2022) - [arXiv]
A linear optimization oracle for zonotope computation
with A. Deza
Computational Geometry 100, 101809 (2022) - [arXiv]
Polytopal balls arising in optimization
with A. Deza and J.-B. Hiriart-Urruty
Contributions to Discrete Mathematics 16(3), 125–138 (2021) - [arXiv]
The diameter of lattice zonotopes
with A. Deza and N. Sukegawa
Proceedings of the American Mathematical Society 148(8), 3507–3516 (2020) - [arXiv]
Elementary moves on lattice polytopes
with J. David and R. Rakotonarivo
Journal of Combinatorial Theory, Series A 172, 105200 (2020) - [arXiv]
Distance between vertices of lattice polytopes
with A. Deza, A. Deza, and Z. Guan
Optimization Letters 14, 309–326 (2020)
Diameter, decomposability, and Minkowski sums of polytopes
with A. Deza
Canadian Mathematical Bulletin 62(4), 741–755 (2019) - [arXiv]
Eccentricities in the flip-graphs of convex polygons
Journal of Graph Theory 92(2), 111–129 (2019) - [arXiv]
Once punctured disks, non-convex polygons, and pointihedra
with H. Parlier
Annals of Combinatorics 22(3), 619–640 (2018) - [arXiv]
Improved bounds on the diameter of lattice polytopes
with A. Deza
Acta Mathematica Hungarica 154(2), 457–469 (2018) - [arXiv]
Modular flip-graphs of one holed surfaces
with H. Parlier
European Journal of Combinatorics 67, 158–173 (2018) - [arXiv]
Flip-graph moduli spaces of filling surfaces
with H. Parlier
Journal of the European Mathematical Society 19(9), 2697–2737 (2017) - [arXiv]
The asymptotic diameter of cyclohedra
with H. Parlier
Israel Journal of Mathematics 219(2), 609–635 (2017) - [arXiv]
A survey on the diameter of lattice polytopes
with A. Deza
Oberwolfach Reports 14(2), 1176–1179 (2017)
The diameter of associahedra
Advances in Mathematics 259, 13–42 (2014) - [arXiv]
The flip-graph of the 4-dimensional cube is connected
Discrete & Computational Geometry 49(3), 511–530 (2013) - [arXiv/supplementary material]
Lifting simplicial complexes to the boundary of convex polytopes
Discrete Mathematics 312(19), 2849–2862 (2012)
Weakly regular subdivisions
Discrete & Computational Geometry 47(1), 106–116 (2012)
A result on flip-graph connectivity
Advances in Geometry 12(1), 63–82 (2012)
Coupled tomography and distinct element method approach to exploring the granular media microstructure in a jamming hourglass
M. Tsukahara, S. Mitrovic, V. Gajdosik, G. Margaritondo, L. Pournin, M. Ramaioli, D. Sage, Y. Hwu, M. Unser and Th. M. Liebling
Physical Review E 77(6), 061306 (2008)
About the influence of friction and polydispersity on the jamming behavior of bead assemblies
L. Pournin, M. Ramaioli, P. Folly and Th. M. Liebling
European Physical Journal E 23(2), 229–235 (2007)
Vertical ordering of rods under vertical vibration
M. Ramaioli, L. Pournin and Th. M. Liebling
Physical Review E 76(2), 021304 (2007)
Constrained paths in the flip-graph of regular triangulations
L. Pournin and Th. M. Liebling
Computational Geometry 37(2), 134–140 (2007)
Three-dimensional distinct element simulation of spherocylinder crystallization
L. Pournin, M. Weber, M. Tsukahara, J.-A. Ferrez, M. Ramaioli and Th. M. Liebling
Granular Matter 7(2-3), 119–126 (2005)
Molecular-dynamics force models for better control of energy dissipation in numerical simulations of dense granular media
L. Pournin, Th. M. Liebling, and A. Mocellin
Physical Review E 65(1), 011302 (2002)

Conference proceedings

Bounds on the diameter of graph associahedra
with J. Cardinal and M. Valencia-Pabon
Proceedings of LAGOS 2021, 239–247 (2021)
A Markov chain for lattice polytopes
with J. David and R. Rakotonarivo
Proceedings of GASCom 2018, 132–139 (2018)
Diameters and geodesic properties of generalizations of the associahedron
with C. Ceballos, T. Manneville, and V. Pilaud
Proceedings of FPSAC 2015, 345–356 (2015)
A combinatorial method to find sharp lower bounds on flip distances
Proceedings of FPSAC 2013, 1–12 (2013)
Particle Shape versus Friction in Granular Jamming
L. Pournin, M. Tsukahara, and Th. M. Liebling
Powders and Grains 2009, AIP Conference Proceedings 1145, 499–502 (2009)
Simple Probabilistic Modeling of Granular Jamming and Validation Using DEM
M. Tsukahara, L. Pournin, and Th. M. Liebling
Powders and Grains 2009, AIP Conference Proceedings 1145, 507–510 (2009)
A generalization of Distinct Element Method to tridimensional particles with complex shapes
L. Pournin and Th. M. Liebling
Powders and Grains 2005 Proceedings vol. II, 1375–1378, A.A.Balkema, Rotterdam (2005)
Numerical and experimental investigation of alignment and segregation of vibrated granular media composed of rods and spheres
M. Ramaioli, L. Pournin and Th. M. Liebling
Powders and Grains 2005 Proceedings vol. II, 1359–1363, A.A.Balkema, Rotterdam (2005)

Book chapters

Sizing the White Whale
with A. Deza and M. Hao
Data Science and Optimization, Fields Institute Communications 91, 209–230 (2026) - [arXiv]
The vertices of primitive zonotopes
with A. Deza and R. Rakotonarivo
Polytopes and Discrete Geometry, Contemporary Mathematics 764, 71–81 (2021)
Voronoi diagrams and Delaunay triangulations: ubiquitous Siamese twins
with Th. M. Liebling
Optimization stories, 419–431, Documenta Mathematica Series, EMS Press (2012)
From spheres to spheropolyhedra: generalized Distinct Element Methodology and algorithm analysis
L. Pournin and Th. M. Liebling
Research Trends in Combinatorial Optimization, 347–363, Springer, Berlin (2009)

Co-authors

Théophile Buffière, Jean Cardinal, Jean-Philippe Chancelier, Cesar Ceballos, Michel de Lara, Julien David, Anna Deza, Antoine Deza, Jean‑Albert Ferrez, Patrick Folly, Vincent Gajdosik, Zhongyan Guan, Mingfei Hao, Jean‑Baptiste Hiriart-Urruty, Yeu‑Kuang Hwu, Thomas Liebling, Zhongyuan Liu, Thibault Manneville, Giorgio Margaritondo, Slobodan Mitrovic, Alain Mocellin, Shmuel Onn, Pallavi Panda, Hugo Parlier, Vincent Pilaud, Sebastian Pokutta, Rado Rakotonarivo, Marco Ramaioli, Daniel Sage, Noriyoshi Sukegawa, Michel Tsukahara, Michael Unser, Mario Valencia-Pabon, Zili Wang, Mats Weber.