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math.CO2026
Szemerédi's theorem with random differences and arithmetic Kakeya
Gabriel Dahia
We prove that there exists an absolute constant such that the following holds for every and . Letting and , with…
math.CO2026
Counting sets with given doubling via dimension
Marcelo Campos, Gabriel Dahia, João Pedro Marciano
We determine, up to a factor of , the number of -sets such that , where and , for small…
math.CO2026
Dense sets without large sumsets
Gabriel Dahia, João Pedro Marciano, Victor Souza
We prove, for all fixed , and all sufficiently large , that there exists with such that for all ${A, B \subset \mat…