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Subcritical monotone cellular automata

https://doi.org/10.1002/rsa.21174

Balister, Paul; Bollobás, Béla; Morris, Robert; Smith, Paul (January 2024, Random Structures & Algorithms)

Abstract We study monotone cellular automata (also known as ‐bootstrap percolation) in with random initial configurations. Confirming a conjecture of Balister, Bollobás, Przykucki and Smith, who proved the corresponding result in two dimensions, we show that the critical probability is non‐zero for all subcritical models.
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The structure and number of Erdős covering systems

https://doi.org/10.4171/JEMS/1357

Balister, Paul; Bollobás, Béla; Morris, Robert; Sahasrabudhe, Julian; Tiba, Marius (June 2023, Journal of the European Mathematical Society)

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On the Erdős covering problem: the density of the uncovered set

https://doi.org/10.1007/s00222-021-01087-5

Balister, Paul; Bollobás, Béla; Morris, Robert; Sahasrabudhe, Julian; Tiba, Marius (April 2022, Inventiones mathematicae)

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The Erdős–Selfridge problem with square-freemoduli

https://doi.org/10.2140/ant.2021.15.609

Balister, Paul; Bollobás, Béla; Morris, Robert; Sahasrabudhe, Julian; Tiba, Marius (January 2021, Algebra & Number Theory)
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Flat Littlewood polynomials exist

https://doi.org/10.4007/annals.2020.192.3.6

Balister, Paul; Bollobás, Béla; Morris, Robert; Sahasrabudhe, Julian; Tiba, Marius (November 2020, Annals of Mathematics)

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