Locality in sumsets

P van Hintum, P Keevash - arXiv preprint arXiv:2304.01189, 2023 - arxiv.org
Motivated by the Polynomial Freiman-Ruzsa (PFR) Conjecture, we develop a theory of
locality in sumsets, with applications to John-type approximation and sets with small …

Isoperimetric inequalities and supercritical percolation on high-dimensional graphs

S Diskin, J Erde, M Kang, M Krivelevich - Combinatorica, 2024 - Springer
It is known that many different types of finite random subgraph models undergo
quantitatively similar phase transitions around their percolation thresholds, and the proofs of …

Phase transitions in isoperimetric problems on the integers

J Briggs, C Wells - arXiv preprint arXiv:2402.14087, 2024 - arxiv.org
Barber and Erde asked the following question: if $ B $ generates $\mathbb Z^ n $ as an
additive group, then must the extremal sets for the vertex/edge-isoperimetric inequality on …

[PDF][PDF] Isoperimetric Inequalities and Supercritical Percolation on High-dimensional Product Graphs

S Diskin, J Erde, M Kang… - Combinatorica, to appear, 2023 - researchgate.net
It is known that many different types of finite random subgraph models undergo
quantitatively similar phase transitions around their percolation thresholds, and the proofs of …

The isoperimetric peak of complete trees

A Bonato, L Mandic, TG Marbach, M Ritchie - arXiv preprint arXiv …, 2024 - arxiv.org
We give exact values and bounds on the isoperimetric peak of complete trees, improving on
known results. For the complete $ q $-ary tree of depth $ d $, if $ q\ge 5$, then we find that …