Results 11 to 20 of about 37 (37)

Local aspects of the Sidorenko property for linear equations

Forum of Mathematics, Sigma
A system of linear equations in $\mathbb {F}_p^n$ is Sidorenko if any subset of $\mathbb {F}_p^n$ contains at least as many solutions to the system as a random set of the same density, asymptotically as $n\to \infty $ .
Daniel Altman
doaj   +1 more source

Relative rank and regularization

Forum of Mathematics, Sigma
We introduce a new concept of rank – relative rank associated to a filtered collection of polynomials. When the filtration is trivial, our relative rank coincides with Schmidt rank (also called strength).
Amichai Lampert, Tamar Ziegler
doaj   +1 more source

Simplices in large sets and directional expansion in ergodic actions

Forum of Mathematics, Sigma
In this paper, we study ergodic $\mathbb {Z}^r$ -actions and investigate expansion properties along cyclic subgroups. We show that under some spectral conditions, there are always directions which expand significantly a given measurable set with ...
Michael Björklund, Alexander Fish
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Asymmetric infinite sumsets in large sets of integers

Forum of Mathematics, Sigma
We show that for any set $A\subset {\mathbb N}$ with positive upper density and any $\ell ,m \in {\mathbb N}$ , there exist an infinite set $B\subset {\mathbb N}$ and some $t\in {\mathbb N}$ so that $\{mb_1 + \ell b_2 ...
Ioannis Kousek
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Partition regularity of Pythagorean pairs

Forum of Mathematics, Pi
We address a core partition regularity problem in Ramsey theory by proving that every finite coloring of the positive integers contains monochromatic Pythagorean pairs (i.e., $x,y\in {\mathbb N}$ such that $x^2\pm y^2=z^2$ for some $z ...
Nikos Frantzikinakis, Oleksiy Klurman, Joel Moreira   +2 more
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Finding product sets in some classes of amenable groups

Forum of Mathematics, Sigma
In [15], using methods from ergodic theory, a longstanding conjecture of Erdős (see [5, Page 305]) about sumsets in large subsets of the natural numbers was resolved.
Dimitrios Charamaras, Andreas Mountakis
doaj   +1 more source

Spectral algorithms in higher-order Fourier analysis

Forum of Mathematics, Sigma
Our goal is to provide simple and practical algorithms in higher-order Fourier analysis which are based on spectral decompositions of operators. We propose a general framework for such algorithms and provide a detailed analysis of the quadratic case. Our
Pablo Candela, Diego González-Sánchez, Balázs Szegedy   +2 more
doaj   +1 more source

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Higher uniformity of bounded multiplicative functions in short intervals on average

Annals of Mathematics, 2023
Tamar Ziegler, Terence Tao, Kaisa Matomäki   +2 more
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On half-factoriality of transfer Krull monoids

Communications in Algebra, 2021
Chao Liu, Salvatore Tringali, Qinghai Zhong   +2 more
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Testing Linear-Invariant Properties

SIAM Journal on Computing, 2022
Jonathan Tidor, Yufei Zhao
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