Recent Submissions

  • Short synchronizing words for random automata 

    Chapuy, Guillaume; Perarnau Llobet, Guillem (Curran Associates, Inc., 2023)
    Conference report
    Open Access
    We prove that a uniformly random automaton with n states on a 2-letter alphabet has a synchronizing word of length with high probability (w.h.p.). That is to say, w.h.p. there exists a word ¿ of such length, and a state ...
  • Block statistics in subcritical graph classes 

    Ralaivaosaona, Dimbinaina; Requile, Clement; Wagner, Stephan (2020)
    Conference report
    Open Access
    We study block statistics in subcritical graph classes; these are statistics that can be defined as the sum of a certain weight function over all blocks. Examples include the number of edges, the number of blocks, and the ...
  • 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 ...
  • 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 ...
  • 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 ...
  • Additive MDS codes 

    Ball, Simeon Michael; Adriaensen, Sam (2022)
    Conference report
    Open Access
    We prove that an additive code over a finite field which has a few projections which are equivalent to a linear code is itself equivalent to a linear code, providing the code is not too short.
  • Showing non-realizability of spheres by distilling a tree 

    Pfeifle, Julián (2021)
    Conference report
    Open Access
    In [Zhe20a], Hailun Zheng constructs a combinatorial 3-sphere on 16 vertices whose graph is the complete 4-partite graph K4;4;4;4. Such a sphere seems unlikely to be realizable as the boundary complex of a 4-dimensional ...
  • Polynomials for marked graphs and the chromatic symmetric function 

    Aliste Prieto, José; Mier Vinué, Anna de; Orellana, Rosa; Zamora, José (Universidad de Cantabria, 2022)
    Conference lecture
    Restricted access - publisher's policy
  • Weak components of the directed configuration model 

    Coulson, Matthew John; Perarnau Llobet, Guillem (Springer, 2021)
    Conference report
    Open Access
    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 ...

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