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16 papers · 1 filter
Harmonic Labeling of Graphs
Itai Benjamini, Van Cyr, Eviatar B. Procaccia +1
Which graphs admit an integer value harmonic function which is injective and surjective onto ? Such a function, which we call harmonic labeling, is constructed when the graph i…
Quantitative relation between noise sensitivity and influences
Nathan Keller, Guy Kindler
A Boolean function is said to be noise sensitive if inserting a small random error in its argument makes the value of the function almost unpredictable. B…
Sums and products along sparse graphs
Noga Alon, Omer Angel, Itai Benjamini +1
In their seminal paper from 1983, Erdős and Szemerédi showed that any distinct integers induce either distinct sums of pairs or that many distinct products, and conje…
Morphic and Automatic Words: Maximal Blocks and Diophantine Approximation
Yann Bugeaud, Dalia Krieger, Jeffrey Shallit
Let $\mb w$ be a morphic word over a finite alphabet , and let be a nonempty subset of . We study the behavior of maximal blocks consisting only of letters from in $\…
Worst Case to Average Case Reductions for Polynomials
Tali Kaufman, Shachar Lovett
A degree- polynomial in variables over a field $\F$ is {\em equidistributed} if it takes on each of its $|\F|$ values close to equally often, and {\em biased} otherwise.…
New Proofs of the Green-Tao-Ziegler Dense Model Theorem: An Exposition
Omer Reingold, Luca Trevisan, Madhur Tulsiani +1
Green, Tao and Ziegler prove ``Dense Model Theorems'' of the following form: if R is a (possibly very sparse) pseudorandom subset of set X, and D is a dense subset of R, then D may…