GAPCOMB  Geometric, Algebraic and Probabilistic Combinatorics
The research of the group focuses on interrelated aspects of combinatorics: Graph theory, Random Graphs, Probabilistic method, Geometric group theory and algebraic methods, Enumerative combinatorics, Combinatorial geometry, and Combinatorial number theory. Some recent research achievements are: Proof of the Maximum Distance Separable codes conjecture for prime fields; solution of a conjecture of Green on the removal lemma for systems of equations in finite fields
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Articles de revista [35]
Recent Submissions

Limiting probabilities of first order properties of random sparse graphs and hypergraphs
(20210818)
Article
Restricted access  publisher's policyLet Gn be the binomial random graph G(n, p = c/n) in the sparse regime, which as is wellknown undergoes a phase transition at c = 1. Lynch (Random Structures Algorithms, 1992) showed that for every first order sentence ... 
An irrationalslope Thompson’s group
(20210101)
Article
Open AccessThe purpose of this paper is to study the properties of the irrationalslope Thompson’s group Ft introduced by Cleary in [11]. We construct presentations, both finite and infinite, and we describe its combinatorial structure ... 
Onto extensions of free groups
(20210407)
Article
Open AccessRationale Cocaine addiction is a chronic relapsing disorder that lacks of an effective treatment. Isoflavones are a family of compounds present in different plants and vegetables like soybeans that share a common chemical ... 
Weak components of the directed configuration model
(Springer, 2021)
Conference report
Restricted access  publisher's policyWe study the threshold for the existence of a linear order weakly connected component in the directed configuration model, confirming analytic but nonrigorous results recently obtained by Kryven [8]. We also establish ... 
On sets defining few ordinary solids
(Springer Nature, 20210504)
Article
Open AccessLet S be a set of n points in real fourdimensional space, no four coplanar and spanning the whole space. We prove that if the number of solids incident with exactly four points of S is less than Kn3 for some K=o(n1/7) ... 
Probabilistic nilpotence in infinite groups
(20210702)
Article
Restricted access  publisher's policyThe ‘degree of kstep nilpotence’ of a finite group G is the proportion of the tuples (x1,…, xk+1 ¿ Gk+1 for which the simple commutator [x1, …, xk+1] is equal to the identity. In this paper we study versions of this for ... 
On Motzkin’s problem in the circle group
(20210901)
Article
Restricted access  publisher's policyGiven a subset D of the interval (0,1), if a Borel set A¿[0,1) contains no pair of elements whose difference modulo 1 is in D, then how large can the Lebesgue measure of A be? This is the analogue in the circle group of a ... 
The expected number of perfect matchings in cubic planar graphs
(Birkhäuser, 20210901)
Part of book or chapter of book
Restricted access  publisher's policyA wellknown conjecture by Lovász and Plummer from the 1970s asserting that a bridgeless cubic graph has exponentially many perfect matchings was solved in the affirmative by Esperet et al. (Adv. Math. 2011). On the other ... 
A polynomialtime reduction from the multigraph isomorphism problem to additive codeequivalence
(20211202)
Article
Open AccessWe present a polynomialtime reduction from the multigraph isomorphism problem to the problem of code equivalence of additive codes over finite extensions of the field with two elements. 
The giant component of the directed configuration model revisited
(20210422)
Article
Open AccessWe prove a law of large numbers for the order and size of the largest strongly connected component in the directed configuration model. Our result extends previous work by Cooper and Frieze (2004). 
Percolation on random graphs with a fixed degree sequence
(20220104)
Article
Open AccessWe consider bond percolation on random graphs with given degrees and bounded average degree. In particular, we consider the order of the largest component after the random deletion of the edges of such a random graph. We ... 
Cycles of given lengths in unicyclic components in sparse random graphs
(Elsevier, 20210401)
Article
Open AccessLet L be subset of {3,4,…} and let Xn,M(L) be the number of cycles belonging to unicyclic components whose length is in L in the random graph G(n,M). We find the limiting distribution of Xn,M(L) in the subcritical regime ...