7 citations · 26 across the 14 of their papers we have counts for
11 papers · 1 filter
The Rado Multiplicity Problem in Vector Spaces over Finite Fields
Juanjo Rué, Christoph Spiegel
We study an analogue of the Ramsey multiplicity problem for additive structures, in particular establishing the minimum number of monochromatic 3-APs in 3-colorings of $\mathbb{F}_…
New Ramsey Multiplicity Bounds and Search Heuristics
Olaf Parczyk, Sebastian Pokutta, Christoph Spiegel +1
We study two related problems concerning the number of homogeneous subsets of given size in graphs that go back to questions of Erdős. Most notably, we improve the upper bounds on…
Independent Chains in Acyclic Posets
Nika Salia, Christoph Spiegel, Casey Tompkins +1
We consider the problem of determining the maximum order of an induced vertex-disjoint union of cliques in a graph. More specifically, given some family of graphs of…
On strong infinite Sidon and sets and random sets of integers
David Fabian, Juanjo Rué, Christoph Spiegel
A set of integers is an -strong Sidon set if the pairwise sums of its elements are far apart by a certain measure depending on , more specifically if $…
On the Odd Cycle Game and Connected Rules
Jan Corsten, Adva Mond, Alexey Pokrovskiy +2
We study the positional game where two players, Maker and Breaker, alternately select respectively and previously unclaimed edges of . Maker wins if she succeeds in cl…
Another Note on Intervals in the Hales-Jewett Theorem
Nina Kamčev, Christoph Spiegel
The Hales-Jewett Theorem states that any -colouring of contains a monochromatic combinatorial line if is large enough. Shelah's proof of the theorem implies that for…
A step beyond Freiman's theorem for set addition modulo a prime
Pablo Candela, Oriol Serra, Christoph Spiegel
Freiman's 2.4-Theorem states that any set satisfying and can be covered by an arithmetic progression of length at most…
On a problem of Sárközy and Sós for multivariate linear forms
Juanjo Rué, Christoph Spiegel
We prove that for pairwise co-prime numbers there does not exist any infinite set of positive integers such that the representation function $r_A (n) = \…
On the optimality of the uniform random strategy
Christopher Kusch, Juanjo Rué, Christoph Spiegel +1
The concept of biased Maker-Breaker games, introduced by Chvátal and Erd{\H o}s, is a central topic in the field of positional games, with deep connections to the theory of random…
A Note on Sparse Supersaturation and Extremal Results for Linear Homogeneous Systems
Christoph Spiegel
We study the thresholds for the property of containing a solution to a linear homogeneous system in random sets. We expand a previous sparse Szémeredi-type result of Schacht to the…
Threshold functions and Poisson convergence for systems of equations in random sets
Juanjo Rué, Christoph Spiegel, Ana Zumalacárregui
We present a unified framework to study threshold functions for the existence of solutions to linear systems of equations in random sets which includes arithmetic progressions, sum…