Geometric, Algebraic and Probabilistic Combinatorics

Publications

See the webpage of the members of the group for the whole list of papers of each researcher.

Highlighted papers of the research team

 Books, chapters and special issues.

S.Ball, O. Serra, A Course in Combinatorics and Graphs. Compact Textbooks in Mathematics, Birkhauser, 2024.

S.Ball. A Course in Algebraic Error-Correcting Codes, Compact Textbooks in Mathematics, Birkhauser, 2020.

S. Ball. Finite Geometry and Combinatorial Applications. London Mathematical Society Student texts 82, Cambridge University Press, 2015.

J. Nesetril, G. Perarnau, J. Rué, O. Serra (Editors). Extended abstracts Eurocomb 2021. Trends in Mathematics -  Research Perspectives CRM Barcelona 14, Birkhäuser, 2021. 

A. Lo, R. Mycroft, G. Perarnau, A. Treglown (Editors). Surveys in combinatorics 2019.  London Mathematical Society Lecture Note Vol. 456, 2019. Cambridge University Press.

 

 2026

S. Ball, R. Vilar, Classical and quantum cyclic redundancy check codes, Adv. Math. Comm. 21: 75–94, 2026.

S. Ball, T. Popatia, Additive codes from linear codes, IEEE Trans. Inf. Theory, to appear.

X.S Cai, G. Perarnau, Minimum stationary values of sparse random directed graphs, Annals Applied Probability to appear.

2025

F. Illingworth, R. Lang, A. Müyesser, O. Parczyk, A. Sgueglia, Spanning spheres in Dirac hypergraphs, Combinatorica 45: 43, 2025.

S. Ball, E. Moreno, R. Simoens, Stabiliser codes over fields of even order, IEEE Trans. Inf. Theory 71: 3707–3718, 2025.

S. Ball, M. Lavrauw, T. Popatia, Griesmer type bounds for additive codes over finite fields, integral and fractional MDS codes, Des. Codes Cryptogr. 93: 175–196, 2025.

K. Abdukhalikov, S. Ball, D. Ho, T. Popatia, Ovoids in the cyclic presentation of PG(3,q), Des. Codes Cryptogr. 93: 4765–4778, 2025.

D. Fabian, P. Morris, T. Szabó, Slow graph bootstrap percolation II: Accelerating properties, J. Comb. Theory Ser. B 172: 44–79, 2025.

C. Bowtell, P. Morris, Y. Pehova, K. Staden, Universality for transversal Hamilton cycles, Bull. Lond. Math. Soc. 57(3): 711–729, 2025.

P. Morris, Clique factors in pseudorandom graphs, J. Eur. Math. Soc. 27(2): 801–875, 2025.

2024

A. Espuny Díaz, P. Morris, G. Perarnau, O. Serra, Speeding up random walk mixing by starting from a uniform vertex,  Electron. J. Probab. 29: 1-25, 2024. 

 J. Delgado, E. Ventura, A. Zakharov, "Relative order and spectrum in free and related groups", Communications in Contemporary Mathematics 26(1):2250066, 2024.

J. Castellví, M. Drmota, M. Noy, C. Requile, Chordal graphs with bounded tree-width, Adv. Appl. Math. 157: 102700, 2024.

M. Noy, C.Requile, J. Rué, Enumeration of rooted 3-connected bipartite planar maps, C. R. Math. 362: 143–158, 2024.

M. Bonamy, M. Delcourt, R.Lang, L. Postle, Edge-colouring graphs with local list sizes, J. Comb. Theory Ser. B 165: 68–96, 2024.

2023

X. S. Cai, P. Caputo, G. Perarnau and M. Quattropani. Rankings in directed configuration models with heavy tailed in-degrees. Annals of Applied Probability, 33(6B):5613–5667, 2023.
M. Coulson and G. Perarnau. Largest component of subcritical random graphs with given degree sequence. Electron. J. Probab. 28: 1-28, 2023. 
G. Chapuy and G. Perarnau. Short Synchronizing Words for Random Automata. Proceedings of the 34th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2023), Florence, Italy, 2023.
S.Ball, A. Centelles, F. Huber: Quantum error-correcting codes and their geometries, Ann.Inst.H.Poincare D Comb.Phys.Interact. 10 2, 337-405, 2023 pdf
S. Ball, G. Gamboa, M. Lavrauw: On additive MDS codes over small fields, Advances in Mathematics of Communications, 17(4):828-844, 2023.
 pdf 
X. S. Cai, G. Perarnau: The diameter of the directed configuration model.  Annales IHP. Probabilites et Statistiques 59(1):244–270, 2023. 
J. Pfeifle: Positive Plücker tree certificates for non-realizability. Experimental Mathematics 33(1):69-85.
R. Lang, N. Sanhueza-Matamala, On sufficient conditions for spanning structures in dense graphs, Proc. Lond. Math. Soc. 127(3): 709–791, 2023.
M. Noy, C. Requile, J. Rué, Enumeration of labelled 4-regular planar graphs II: Asymptotics, Eur. J. Comb. 110: 103661, 2023.
J. Aliste-Prieto, A. de Mier, R. Orellana, J. Zamora, Marked graphs and the chromatic symmetric function, SIAM J. Discrete Math. 37, 2023.
 

2022

S. Ball, R. Vilar: The geometry of Hermitian self-orthogonal codes, Journal of Geometry, 113, Article number: 7 (2022). 

S. Ball, R. Vilar: Determining when a truncated generalised Reed-Solomon code is Hermitian self-orthogonal, IEEE Transactions on Information Theory, 68: 3796--3805 (2022).  

N. Fountoulakis, F. Joos and G. Perarnau. Percolation on random graphs with a fixed degree sequence. SIAM Journal on Discrete Mathematics, 36 (1):1-46, (2022).

J. Delgado, E. Ventura: Free-times-abelian groups: Stallings automata, intersections and index. Publicacions Matemàtiques 66 (2): 789  - 830 (2022).

J. Delgado, E. Ventura,: A list of applications of Stallings automata, Transactions on Combinatorics 11(3): 181--235 (2022).

Y. Chang, J. Han, P. Morris, Y. Kohayakawa, G. Oliveira Mota: Factors in randomly perturbed hypergraphs, Random Structures & Algorithms, 60 (2), 153-165, (2022).

H. Hàn, J. Han and P. Morris: Factors and loose Hamilton cycles in sparse pseudo-random hypergraphs, Random Structures & Algorithms, 61 (1), 101-125, (2022).

G. Fiz-Pontiveros, S. Griffiths, M. Secco, O. Serra: Deviation probabilities for arithmetic progressions and other regular discrete structures. Random structures and algorithms 60 (3): 367 - 405 (2022).

M. Noy, J. Rué, C.Requilé: On the expected number of perfect matchings in cubic planar graphs.  Publicacions Matemàtiques 66 (1): 325-353 (2022).

 

2021

S.Ball, E. Jimenez. On sets defining few ordinary solids. Discrete and Computational Geometry 66:  68-91 (2021).

P. Burillo, B. Nucinkis, L. Reeves. An irrational-slope Thompson’s group. Publicacions Matemàtiques 65: 809-839 (2021).

A. Lladó, H. Mokhtar, O. Serra, S. Zhou. Distance-constrained labellings of Cartesian products of graphs. Discrete Applied Mathematics 304: 375-383 (2021).

P. Candela, C. Catalá, J. Rué, O. Serra. On Motzkin's problem in the circle group. Vinogradov Memorial Volume of the Proceedings of the Steklov Institute of Mathematics 314, 44-63 (2021). (Russian version here)

G. Cao-Labora, J. Rué, C. Spiegel. An Erdös-Fuchs Theorem for Ordered Representation Functions.  The Ramanujan Journal 56, 183-201 (2021).

G. Chapuy and G. Perarnau. On the number of coloured triangulations of d-manifolds. Discrete & Computational Geometry 65: 601-617 (2021).

D. Fabian, J. Rué, C. Spiegel. On strong infinite Sidon and Bh sets and random sets of integers. Journal of Combinatorial Theory, Series A, 182, Art. 105460 (2021).

S. Mijares, E. Ventura, "Onto extensions of free groups", Journal of Groups, Complexity, Cryptology  13(1) (2021), 2:1--2:15.

A. Martino, M. Tointon, M. Valiunas, E. Ventura: Probabilistic nilpotence in infinite groups. Israel Journal of Mathematics 244: 539-588 (2021).

M. Roy, E. Ventura: Degrees of compression and inertia for free-abelian times free groups. Journal of Algebra 568: 241-272 (2021).

 J. Pfeifle: Large final polynomial from integer programming. ACM Communications in Computer Algebra 2021, 55 (3): 82-86 (2021).

 

2020 

A. Abiad, S. Gribling, D. Lahaye, M. Mnich, G. Regts, L. Vena, G. Verweij, P. Zwaneweld. On the complexity of solving a decision problem with flow-depending costs: The case of the IJsselmeer dike. Discrete Optimization 37, Art. 100565 (2020).

K. Böröczky, M. Matolcsi, I. Ruzsa, F. Santos, O. Serra. Triangulations and a Discrete Brunn–Minkowski Inequality in the Plane. Discrete and Computational Geometry 64 (2): 396-426 (2020).

M. Delcourt, M. Heinrich, G. Perarnau. The Glauber dynamics for edges colourings of trees.  Random Structures & Algorithms, 57(4):1050--1076  (2020). 

J.Rué, C. Spiegel: On a problem of Sárközy and Sós for multivariate linear forms. Revista Matemática Iberoamericana  36 (7): 2107–2119 (2020). 

J. Cilleruelo, O. Serra, M. Wötzel: Sidon set systems. Revista Matemática Iberoamericana 36 (5): 1527–1548 (2020).

M. Noy, C. Requilé, J. Rué: Further results on random cubic planar graphs. Random Structures and Algorithms 56 (3): 892-924 (2020). 

M. Roy, E. Ventura: Fixed subgroups and computation of auto-fixed closures in free-abelian times free groups",  J. of Pure and Appl. Alg. 224 (4): 106-210 (2020).

J. Wu, E. Ventura, Q. Zhang, "Fixed subgroups in direct products of surface groups of Euclidean type", Communications in Algebra 48 (7):  3003 - 3010 (2020).

S. Ball, B. Csajbok. On sets of points with few odd secants. Combinatorics, Probability, Computing, 29: 31-43 (2020).

G. Chapuy and G. Perarnau. Local convergence and stability of tight bridge-addable graph classes. Canadian Journal of Mathematics 72(3):563--601 (2020).

M. Coulson, P. Keevash, G. Perarnau, L. Yepremyan. Rainbow factors in hypergraphs. Journal of Combinatorial Theory, Series A 172:105--184 (2020). 

 

2019

C. Kusch, J. Rué, C. Spiegel, T. Szabó: On the optimality of the uniform random strategy. Random Structures and Algorithms 55 (2): 371-401 (2019) .

M. Noy, C. Requilé, J. Rué: Enumeration of labelled 4-regular planar graphs. To appear at Proceedings of the London Mathematical Society 119 (2): 358-378

G. Chapuy, G. Perarnau. Connectivity in bridge-addable graph classes: the McDiarmid-Steger-Welsh conjecture. J. of Combinatorial Theory, Series B 136 (C):44-71 (2019).

M. Coulson, G. Perarnau. Rainbow matchings in Dirac bipartite graphs. Random Structures and Algorithms  55(2):271-289 (2019).

S. Ball, M. Lavrauw. Arcs in finite projective spaces, EMS Surveys in Mathematical Science, 6,133--172 (2019) . 

2018

S. Ball: On sets defining few ordinary planes. Discrete and Computational Geometry, 60 (2018), p. 220-253.

S. Ball: Extending small arcs to large arcs, European Journal of Mathematics, 4 (2018) 8-25.

S. Ball: Review of Larry Guth's "Polynomial Methods in Combinatorics" in Jahresbericht der Deutschen Mathematiker-Vereinigung, 120 (2018) 147-150. 

S. Ball, M. Lavrauw: Planar arcs, Journal of Combinatorial Theory, Series A, 160 (2018) 261-287. 

A. Lladó: Decomposing almost complete graphs by random tree. Journal of combinatorial theory, Series A, Vol. 154, p. 406-421.

P. Heinig, T. Müller, M. Noy, A. Taraz: Logical limit laws for minor-closed classes of graphs. Journal of combinatorial theory. Series B, Vol. 130, p. 158-206.

T. Müller, M. Noy: The first order convergence fails for perfect random graphs. Random Structures & Algorithms 53 (4) (2018): 717-727.

J. Rué, C. Spiegel, A. Zumalacárregui Threshold functions for systems of equations on random sets. Mathematische Zeitschrift 288 (1-2) (2018), 333-36

 J. Delgado, E. Ventura, A. Zakharov, "Intersection problem for Droms RAAGs", International Journal of Algebra and Computation 28 (2018), 1129--1162

 

 Published Papers (Selection 2014-2017)

Y. Antolín, A. Martino, E. Ventura, "Degree of commutativity of infinite groups", Proceedings of the American Mathematical Society 145 (2): 479 - 485 (2017)

B. Cavallo, J. Delgado, D. Kahrobaei, E. Ventura, "Algorithmic recognition of infinite cyclic extensions", Journal of Pure and Applied Algebra 221 (2017), 2157--2179

M. Drmota, L. Ramos, J. Rué: Subgraph statistics in subcritical graph classes. Random Structures & Algorithms 51 (4) (2017): 631-673.

J. Martí-Farré, A. de Mier: Transformation and decomposition of clutters into matroids. Advances in Mathematics 312 (2017), 286–314.

 J. Burillo, F. Matucci, E. Ventura: The conjugacy problem in extensions of Thompson's group F. Israel Journal of Mathematics 216 (2017), 15–59.

Y. Antolín, A. Martino, E. Ventura: Degree of commutativity of infinite groups. Proceedings of the American Mathematical Society 145 (2017), 479–485.

J. Rué, O. Serra, Ll. Vena: Counting configuration-free sets on groups. European Journal of Combinatorics 66 (2017), 281-307.

S. Ball, J. de Beule: On subsets of the Normal Rational Curve. IEEE Transactions on Information Theory 63 (2017), 3658–3662.

S. Ball: Finite geometry and combinatorial applications. Cambridge University Press 2015. 

Y. Antolín, J. Burillo, A. Martino: Conjugacy in Houghton's groups. Publicacions Matemàtiques 59 (2015), 3-16.

M. Noy, J. Rué, V. Ravelomanana: On the probability of planarity of a random graph near the critical point. Proceedings of the American Mathematical Society 143 (2015), 925–936.

K. Böröczky, F. Santos, O. Serra: On sumsets and convex hull. Pages: Discrete and Computational Geometry 52 (2014), 705–729.

M. Drmota, O. Giménez, M. Noy, K. Panagiotou, A. Steger: The maximum degree of random planar graphs. Proceedings of the London Mathematical Society 109 (2014), 892-920.