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papers

Publications (18)

math.CO2021

Partial associativity and rough approximate groups

W. T. Gowers, Jason Long

Suppose that a binary operation $\circ$ on a finite set $X$ is injective in each variable separately and also associative. It is easy to prove that $(X, \circ)$ must be a group. In…

math.CO2019

A note on the Brown--ErdÅs--SÃ³s conjecture in groups

Jason Long

We show that a dense subset of a sufficiently large group multiplication table contains either a large part of the addition table of the integers modulo some $k$ , or the entire mul…

math.CO2018

The largest projective cube-free subsets of $Z_{2^{n}}$

Jason Long, Adam Zsolt Wagner

In the Boolean lattice, Sperner's, ErdÅs's, Kleitman's and Samotij's theorems state that families that do not contain many chains must have a very specific layered structure. We s…

cs.LG2022

Robust Counterfactual Explanations for Tree-Based Ensembles

Sanghamitra Dutta, Jason Long, Saumitra Mishra +2

Counterfactual explanations inform ways to achieve a desired outcome from a machine learning model. However, such explanations are not robust to certain real-world changes in the u…

math.CO2019

The extremal number of Venn diagrams

Peter Keevash, Imre Leader, Jason Long +1

We show that there exists an absolute constant $C > 0$ such that any family $F \subset {0, 1}^{n}$ of size at least $C n^{3}$ has dual VC-dimension at least 3. Equivalently, eve…

math.RT2021

Linear characters of Sylow subgroups of symmetric groups

Eugenio Giannelli, Stacey Law, Jason Long

Let $p$ be any prime. Let $P_{n}$ be a Sylow $p$ -subgroup of the symmetric group $S_{n}$ . Let $I ¨ $ and $I ¨ $ be linear characters of $P_{n}$ and let $N$ be the normaliser of $P_{n}$ in $S_n…