Ashna Wright

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math.CO2023

An Approximate Counting Version of the Multidimensional Szemerédi Theorem

Natalie Behague, Joseph Hyde, Natasha Morrison +2

For any fixed $d \geq 1$ and subset $X$ of $N^{d}$ , let $r_{X} (n)$ be the maximum cardinality of a subset $A$ of ${1, \dots, n}^{d}$ which does not contain a subset of the form $\…

math.CO2023

Improved bounds for cross-Sperner systems

Natalie Behague, Akina Kuperus, Natasha Morrison +1

A collection of families $(F_{1}, F_{2}, \dots, F_{k}) \in P ([n])^{k}$ is cross-Sperner if there is no pair $i \neq = j$ for which some $F_i…