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

  • Quantum error-correcting codes and their geometries 

    Ball, Simeon Michael; Centelles Tarrés, Aina; Huber, Felix (European Mathematical Society (EMS), 2023-02-10)
    Article
    Open Access
    This is an expository article aiming to introduce the reader to the underlying mathematics and geometry of quantum error correction. Information stored on quantum particles is subject to noise and interference from the ...
  • Cut vertices in random planar maps 

    Drmota, Michael; Noy Serrano, Marcos; Stufler, Benedikt (2023-09-22)
    Article
    Open Access
    The main goal of this paper is to determine the asymptotic behavior of the number X n of cut-vertices in random planar maps with n edges. It is shown that X n / n ¿ c in probability (for some explicit c > 0 ). For so-called ...
  • The rado multiplicity problem in vector spaces over finite fields 

    Rué Perna, Juan José; Spiegel, Christoph (Muni press, 2023)
    Conference lecture
    Open Access
    We study an analogue of the Ramsey multiplicity problem for additive structures, establishing the minimum number of monochromatic $3$-APs in $3$-colorings of $\mathbb{F}_3^n$ and obtaining the first non-trivial lower bound ...
  • Product-free sets in the free group 

    Ortega Sánchez Colomer, Miquel; Rué Perna, Juan José; Serra Albó, Oriol (2023)
    Conference lecture
    Open Access
    We prove that product-free sets of the free group over a finite alphabet have max-imum density1/2with respect to the natural measure that assigns total weight oneto each set of irreducible words of a given length. This ...
  • Random cubic planar maps 

    Drmota, Michael; Noy Serrano, Marcos; Requile, Clement; Rué Perna, Juan José (2023-06-30)
    Article
    Open Access
    We analyse uniform random cubic rooted planar maps and obtain limiting distributions for several parameters of interest. From the enumerative point of view, we present a unified approach for the enumeration of several ...
  • Enumeration of labelled 4-regular planar graphs II: asymptotics 

    Noy Serrano, Marcos; Requile, Clement; Rué Perna, Juan José (2023-05)
    Article
    Open Access
    This work is a follow-up of the article (Noy et al., 2019), where the authors solved the problem of counting labelled 4-regular planar graphs. In this paper, we obtain a precise asymptotic estimate for the number of labelled ...
  • Stallings automata and applications : BGSMath graduate course 

    Delgado Rodríguez, Jordi; Ventura Capell, Enric; Weil, Pascal (2023-02-15)
    Research report
    Open Access
    The theory of Stallings automata provides a neat geometric representation of subgroups of the free group, and constitutes the modern —and probably the most natural and fruitful — approach to their study. Moreover, if the ...
  • Chordal graphs with bounded tree-width 

    Castellví Foguet, Jordi; Drmota, Michael; Noy Serrano, Marcos; Requile, Clement (Masaryk University, 2023)
    Conference lecture
    Open Access
    Given $t\ge 2$ and $0\le k\le t$, we prove that the number of labelled $k$-connected chordal graphs with $n$ vertices and tree-width at most $t$ is asymptotically $c n^{-5/2} \gamma^n n!$, as $n\to\infty$, for some constants ...
  • Intersection configurations in free and free times free-abelian groups 

    Delgado Rodríguez, Jordi; Roy, Mallika; Ventura Capell, Enric (Cambridge University Press, 2023-09-11)
    Article
    Restricted access - publisher's policy
    In this paper, we study intersection configurations – which describe the behaviour of multiple (finite) intersections of subgroups with respect to finite generability – in the realm of free and free times free-abelian ...
  • Extremal families for Kruskal-Katona Theorem 

    Serra Albó, Oriol; Vena Cros, Lluís (2019)
    Conference report
    Open Access
    Given a set of size $n$ and a positive integer $k<n$, Kruskal--Katona theorem gives the minimum size of the shadow of a family $S$ of $k$-sets of $[n]$ in terms of the cardinality of $S$. We give a characterization of the ...
  • Big Ramsey degrees of 3-uniform hypergraphs 

    Balko, Martin; Chodounsky, David; Hubicka, Jan; Konecny, Matej; Vena Cros, Lluís (2019)
    Conference report
    Open Access
    Given a countably infinite hypergraph $\mathcal R$ and a finite hypergraph $\mathcal A$, the \emph{big Ramsey degree} of $\mathcal A$ in $\mathcal R$ isthe least number $L$ such that, for every finite $k$ and every ...
  • The canonical Tutte polynomial for signed graphs 

    Goodall, Andrew; Litjens, Bart; Regts, Guus; Vena Cros, Lluís (2019)
    Conference report
    Open Access
    We construct a new polynomial invariant for signed graphs, the trivariate Tutte polynomial, which contains among its evaluations the number of proper colorings and the number of nowhere-zero flows. In this, it parallels ...

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