Mohamed Omar

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math.CO2022

Sets Avoiding Full-Rank Three-Point Patterns in $(F_{q}^{n})^{k}$ Are Exponentially Small

Mohamed Omar

We prove that if a subset of $(F_{q}^{n})^{k}$ (with $q$ an odd prime power) avoids a full-rank three-point pattern $x, x + M_{1} d, x + M_{2} d$ then it is ex…

math.CO2022

Partition Rank and Partition Lattices

Mohamed Omar

We introduce a universal approach for applying the partition rank method, an extension of Tao's slice rank polynomial method, to tensors that are not diagonal. This is accomplished…

Sets Avoiding Full-Rank Three-Point Patterns in (Fqn​)k Are Exponentially Small

Partition Rank and Partition Lattices

Sets Avoiding Full-Rank Three-Point Patterns in $(F_{q}^{n})^{k}$ Are Exponentially Small