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math.CO2022
Local aspects of the Sidorenko property for linear equations
Daniel Altman
A system of linear equations in is \textit{Sidorenko} if any subset of contains at least as many solutions to the system as a random set of the sa…
math.CO2022
On the smallest gap in a sequence with Poisson pair correlations
Daniel Altman, Zachary Chase
We prove that any increasing sequence of real numbers with average gap and Poisson pair correlations has some gap that is at least . This improves upon a result of…
math.CO2022
On a question of Alon
Daniel Altman
A system of linear equations in is \textit{common} if every two-colouring of yields at least as many monochromatic solutions as a random two-colou…
math.CO2022
A non-flag arithmetic regularity lemma and counting lemma
Daniel Altman
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…