Zobrazeno 1 - 10
of 71
pro vyhledávání: '"Kanellopoulos, Vassilis"'
A conjecture of Leader, Russell and Walters in Euclidean Ramsey theory says that a finite set is Ramsey if and only if it is congruent to a subset of a set whose symmetry group acts transitively. As they have shown the ``if" direction of their conjec
Externí odkaz:
http://arxiv.org/abs/1905.04892
Publikováno v:
Acta Arithmetica 203 (2022), 251-270
We show that, under some mild hypotheses, the Gowers uniformity norms (both in the additive and in the hypergraph setting) are essentially equivalent to certain weaker norms which are easier to understand. We present two applications of this equivale
Externí odkaz:
http://arxiv.org/abs/1610.00487
Publikováno v:
Fundamenta Mathematicae 248 (2020), 49-77
We consider some variants of the Gowers box norms, introduced by Hatami, and show their relevance in the context of sparse hypergraphs. Our main results are the following. Firstly, we prove a generalized von Neumann theorem for $L_p$ graphons. Second
Externí odkaz:
http://arxiv.org/abs/1510.07140
Publikováno v:
Fundamenta Mathematicae 240 (2018), 265-299
We study sparse hypergraphs which satisfy a mild pseudorandomness condition known as $L_p$ regularity. We prove appropriate regularity and counting lemmas, and we extend the relative removal lemma of Tao in this setting. This answers a question of Bo
Externí odkaz:
http://arxiv.org/abs/1510.07139
Publikováno v:
Journal of Functional Analysis 270 (2016), 609-620
We prove a concentration inequality which asserts that, under some mild regularity conditions, every random variable defined on the product of sufficiently many probability spaces exhibits pseudorandom behavior.
Externí odkaz:
http://arxiv.org/abs/1410.5965
Publikováno v:
The Electronic Journal of Combinatorics 23 (2016), Research Paper P3.11, 1-24
We prove a variant of the abstract probabilistic version of Szemer\'edi's regularity lemma, due to Tao, which applies to a number of structures (including graphs, hypergraphs, hypercubes, graphons, and many more) and works for random variables in $L_
Externí odkaz:
http://arxiv.org/abs/1410.5966
Publikováno v:
Journal of Combinatorial Theory, Series A 127 (2014), 176-223
For every integer $k\geq 2$ let $[k]^{<\mathbb{N}}$ be the set of all words over $k$, that is, all finite sequences having values in $[k]:=\{1,...,k\}$. A Carlson-Simpson tree of $[k]^{<\mathbb{N}}$ of dimension $m\geq 1$ is a subset of $[k]^{<\mathb
Externí odkaz:
http://arxiv.org/abs/1303.5001
Publikováno v:
Combinatorica 34 (2014), 427-470
A tree $T$ is said to be homogeneous if it is uniquely rooted and there exists an integer $b\meg 2$, called the branching number of $T$, such that every $t\in T$ has exactly $b$ immediate successors. A vector homogeneous tree $\mathbf{T}$ is a finite
Externí odkaz:
http://arxiv.org/abs/1209.4988
Publikováno v:
International Mathematics Research Notices 12 (2014), 3340-3352
We give a purely combinatorial proof of the density Hales--Jewett Theorem that is modeled after Polymath's proof but is significantly simpler. In particular, we avoid the use of the equal-slices measure and work exclusively with the uniform measure.<
Externí odkaz:
http://arxiv.org/abs/1209.4986
Publikováno v:
Journal of the European Mathematical Society 16 (2014), 2097-2164
We prove a density version of the Carlson--Simpson Theorem. Specifically we show the following. For every integer $k\geq 2$ and every set $A$ of words over $k$ satisfying \[\limsup_{n\to\infty} \frac{|A\cap [k]^n|}{k^n}>0\] there exist a word $c$ ove
Externí odkaz:
http://arxiv.org/abs/1209.4985