Zobrazeno 1 - 10
of 4 130
pro vyhledávání: '"regularity lemma"'
Autor:
Pillay, Anand, Stonestrom, Atticus
We give an 'arithmetic regularity lemma' for groups definable in finite fields, analogous to Tao's 'algebraic regularity lemma' for graphs definable in finite fields. More specifically, we show that, for any $M>0$, any finite field $\mathbf{F}$, and
Externí odkaz:
http://arxiv.org/abs/2412.11206
Autor:
Tong, Mervyn
Since K\H{o}v\'ari, S\'os, and Tur\'an proved upper bounds for the Zarankiewicz problem in 1954, much work has been undertaken to improve these bounds, and some have done so by restricting to particular classes of graphs. In 2017, Fox, Pach, Sheffer,
Externí odkaz:
http://arxiv.org/abs/2410.13695
Autor:
Garbe, Frederik, Hladký, Jan
It is well-known that if $(A,B)$ is an $\tfrac{\varepsilon}{2}$-regular pair (in the sense of Szemer\'edi) then there exist sets $A'\subset A$ and $B'\subset B'$ with $|A'|\leq \varepsilon|A|$ and $|B'|\leq \varepsilon|B|$ so that the degrees of all
Externí odkaz:
http://arxiv.org/abs/2410.05023
Autor:
Rubin, Natan
We use the polynomial method of Guth and Katz to establish stronger and {\it more efficient} regularity and density theorems for such $k$-uniform hypergraphs $H=(P,E)$, where $P$ is a finite point set in ${\mathbb R}^d$, and the edge set $E$ is deter
Externí odkaz:
http://arxiv.org/abs/2407.15518
Autor:
Chernikov, Artem, Towsner, Henry
We investigate various forms of (model-theoretic) stability for hypergraphs and their corresponding strengthenings of the hypergraph regularity lemma with respect to partitions of vertices. On the one hand, we provide a complete classification of the
Externí odkaz:
http://arxiv.org/abs/2402.07870
Autor:
Conant, G., Terry, C.
This expository article is based on two lectures given by the first author at the Fields Institute in the Fall 2021 Thematic Program on Trends in Pure and Applied Model Theory. We give a detailed proof of a qualitative version of the Mallaris-Shelah
Externí odkaz:
http://arxiv.org/abs/2308.16809
Autor:
Altman, Daniel
Green and Tao's arithmetic regularity lemma and counting lemma together apply to systems of linear forms which satisfy a particular algebraic criterion known as the `flag condition'. We give an arithmetic regularity lemma and counting lemma which app
Externí odkaz:
http://arxiv.org/abs/2209.14083
Autor:
MALLIARIS, M., SHELAH, S.
Publikováno v:
The Bulletin of Symbolic Logic, 2021 Dec 01. 27(4), 415-425.
Externí odkaz:
https://www.jstor.org/stable/27107135
We present a new approach for finding matchings in dense graphs by building on Szemer\'edi's celebrated Regularity Lemma. This allows us to obtain non-trivial albeit slight improvements over longstanding bounds for matchings in streaming and dynamic
Externí odkaz:
http://arxiv.org/abs/2207.09354
Autor:
Chevalier, Alexis, Levi, Elad
Szemer\'edi's regularity lemma is a powerful tool in graph theory. It states that for every large enough graph, there exists a partition of the edge set with bounded size such that most induced subgraphs are quasirandom. When the graph is a definable
Externí odkaz:
http://arxiv.org/abs/2204.01158