Now showing items 1-5 of 5

  • A Note on sparse supersaturation and extremal results for linear homogeneous systems 

    Spiegel, Christoph (2017-08-25)
    Article
    Open Access
    We study the thresholds for the property of containing a solution to a linear homogeneous system in random sets. We expand a previous sparse Sz\'emeredi-type result of Schacht to the broadest class of matrices possible. ...
  • On a problem of Sárközy and Sós for multivariate linear forms 

    Rué Perna, Juan José; Spiegel, Christoph (2018-07-01)
    Article
    Restricted access - publisher's policy
    We prove that for pairwise co-prime numbers k1,...,kd = 2 there does not exist any infinite set of positive integers A such that the representation function rA(n) = #{(a1,...,ad) ¿ Ad : k1a1 + ... + kdad = n} becomes ...
  • On the optimality of the uniform random strategy 

    kush, Christopher; Rué Perna, Juan José; Spiegel, Christoph; Szabó, T. (2018-01-01)
    Article
    Restricted access - publisher's policy
    Biased Maker-Breaker games, introduced by Chvátal and Erdos, are central to the field of positional games and have deep connections to the theory of random structures. The main questions are to determine the smallest bias ...
  • Random strategies are nearly optimal for generalized van der Waerden Games 

    Kusch, C.; Rué Perna, Juan José; Spiegel, Christoph; Szabó, T. (2017-08-01)
    Article
    Restricted access - publisher's policy
    In a (1 : q) Maker-Breaker game, one of the central questions is to find (or at least estimate) the maximal value of q that allows Maker to win the game. Based on the ideas of Bednarska and Luczak [Bednarska, M., and T. ...
  • Threshold functions and Poisson convergence for systems of equations in random sets 

    Rué Perna, Juan José; Spiegel, Christoph; Zumalacárregui, Ana (2017-05-10)
    Article
    Open Access
    We study threshold functions for the existence of solutions to linear systems of equations in random sets and present a unified framework which includes arithmetic progressions, sum-free sets, Bh[g]Bh[g]-sets and Hilbert ...