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

Recent Submissions

  • Limiting probabilities of first order properties of random sparse graphs and hypergraphs 

    Larrauri Borroto, Lázaro Alberto; Müller, Tobias; Noy Serrano, Marcos (2021-08-18)
    Article
    Restricted access - publisher's policy
    Let Gn be the binomial random graph G(n, p = c/n) in the sparse regime, which as is well-known undergoes a phase transition at c = 1. Lynch (Random Structures Algorithms, 1992) showed that for every first order sentence ...

  • An irrational-slope Thompson’s group 

    Burillo Puig, José; Nucinkis, Brita; Reeves, Lawrence (2021-01-01)
    Article
    Open Access
    The purpose of this paper is to study the properties of the irrational-slope 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 

    Ventura Capell, Enric; Mijares, Sebastià (2021-04-07)
    Article
    Open Access
    Rationale 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 

    Coulson, Matthew John; Perarnau Llobet, Guillem (Springer, 2021)
    Conference report
    Restricted access - publisher's policy
    We study the threshold for the existence of a linear order weakly connected component in the directed configuration model, confirming analytic but non-rigorous results recently obtained by Kryven [8]. We also establish ...

  • On sets defining few ordinary solids 

    Ball, Simeon Michael; Jiménez Meroño, Enrique (Springer Nature, 2021-05-04)
    Article
    Open Access
    Let S be a set of n points in real four-dimensional 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 

    Ventura Capell, Enric; Martino, Armando; Tointon, Matthew C.H.; Valiunas, Motiejus (2021-07-02)
    Article
    Restricted access - publisher's policy
    The ‘degree of k-step 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 

    Candela Pokorna, Pablo; Catalá, Carlos; Rué Perna, Juan José; Serra Albó, Oriol (2021-09-01)
    Article
    Restricted access - publisher's policy
    Given 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 

    Rué Perna, Juan José; Requile, Clement; Noy Serrano, Marcos (Birkhäuser, 2021-09-01)
    Part of book or chapter of book
    Restricted access - publisher's policy
    A well-known 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 polynomial-time reduction from the multi-graph isomorphism problem to additive codeequivalence 

    Ball, Simeon Michael; Dixon, James (2021-12-02)
    Article
    Open Access
    We present a polynomial-time reduction from the multi-graph 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 

    Cai, Xing Shi; Perarnau Llobet, Guillem (2021-04-22)
    Article
    Open Access
    We 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 

    Fountoulakis, Nikolaos; Joos, Felix; Perarnau Llobet, Guillem (2022-01-04)
    Article
    Open Access
    We 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 

    Noy Serrano, Marcos; Rasendrahasina, Vonjy; Ravelomanana, Vlady; Rué Perna, Juan José (Elsevier, 2021-04-01)
    Article
    Open Access
    Let 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 ...

View more