Exploració per autor "Spiegel, Christoph"
Ara es mostren els items 1-12 de 12
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A Note on sparse supersaturation and extremal results for linear homogeneous systems
(2017-08-25)
Article
Accés obertWe 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. ... -
A step beyond Freiman’s theorem for set addition modulo a prime
(2020-01-01)
Article
Accés obertFreiman’s 2.4-Theorem states that any set A¿Zp satisfying |2A|=2.4|A|-3 and |A|<p/35 can be covered by an arithmetic progression of length at most |2A|-|A|+1. A more general result of Green and Ruzsa implies that this ... -
Additive structures and randomness in combinatorics
(Universitat Politècnica de Catalunya, 2020-07-03)
Tesi
Accés obertArithmetic Combinatorics, Combinatorial Number Theory, Structural Additive Theory and Additive Number Theory are just some of the terms used to describe the vast field that sits at the intersection of Number Theory and ... -
Additive volume of sets contained in few arithmetic progressions
(De Gruyter, 2019-03-06)
Article
Accés obertA conjecture of Freiman gives an exact formula for the largest volume of a finite set A of integers with given cardinality k=|A| and doubling T=|2A|. The formula is known to hold when T=3k-4, for some small range over 3k-4 ... -
An Erdös–Fuchs theorem for ordered representation functions
(2020-10-28)
Article
Accés obertLetk=2 be a positive integer. We study concentration results for the ordered representationfunctionsr=k(A, n) = #{(a1= ··· =ak)¿ Ak:a1+···+ak=n}andr<k(A, n) = #{(a1<···<ak)¿ Ak:a1+···+ak=n}for any infinite set ... -
On a problem of Sárközy and Sós for multivariate linear forms
(2018-07-01)
Article
Accés obertWe 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 a problem of Sárközy and Sós for multivariate linear forms
(2020-03-18)
Article
Accés obertWe 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 constant for n large ... -
On strong infinite Sidon and Bh sets and random sets of integers
(2021-04-21)
Article
Accés obertA set of integers S ¿ N is an a–strong Sidon set if the pairwise sums of its elements are far apart by a certain measure depending on a, more specifically if (x + w) - (y + z) = max{xa, ya, za, wa} for every x, y, z, ... -
On the optimality of the uniform random strategy
(2018-01-01)
Article
Accés restringit per política de l'editorialBiased 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
(2017-08-01)
Article
Accés obertIn 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. ... -
The rado multiplicity problem in vector spaces over finite fields
(Muni press, 2023)
Comunicació de congrés
Accés obertWe 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 ... -
Threshold functions and Poisson convergence for systems of equations in random sets
(2017-05-10)
Article
Accés obertWe 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 ...
