About

I'm currently a Heilbronn Research Fellow at the University of Bristol. Before my current role I spent 8 years at the University of Oxford, first as an undergraduate studying for an MMath and then as a postgraduate studying for a DPhil under the supervision of Alex Scott.

My main research interests are extremal and probabilistic combinatorics.

Papers

A note on the invertibility of oriented graphs
Natalie Behague Tom Johnston Natasha Morrison Shannon Ogden
Submitted
2024+
@article{behague2024invertibility, title={A note on the invertibility of oriented graphs}, author={Behague, Natalie and Johnston, Tom and Morrison, Natasha and Ogden, Shannon}, journal={arXiv preprint arXiv:2404.10663}, year={2024} }
A polynomial upper bound for poset saturation
Paul Bastide Carla Groenland Maria-Romina Ivan Tom Johnston
European Journal of Combinatorics
2024
@article{bastide2024polynomial, title={A polynomial upper bound for poset saturation}, author={Bastide, Paul and Groenland, Carla and Ivan, Maria-Romina and Johnston, Tom}, journal={European Journal of Combinatorics}, year={2024} }
Game connectivity and adaptive dynamics
Tom Johnston Michael Savery Alex Scott Bassel Tarbush
Submitted
2023+
@article{johnston2023game, title={Game Connectivity and Adaptive Dynamics}, author={Johnston, Tom and Savery, Michael and Scott, Alex and Tarbush, Bassel}, journal={arXiv preprint arXiv:2309.10609}, year={2023} }
Counting graphic sequences via integrated random walks
Paul Balister Serte Donderwinkel Carla Groenland Tom Johnston Alex Scott
Submitted
2023+
@article{balister2023counting, title={Counting graphic sequences via integrated random walks}, author={Balister, Paul and Donderwinkel, Serte and Groenland, Carla and Johnston, Tom and Scott, Alex}, year={2023}, journal={arXiv preprint arXiv:2301.07022}, }
Shotgun assembly of random graphs
Tom Johnston Gal Kronenberg Alexander Roberts Alex Scott
Submitted
2022+
@article{johnston2022shotgun, title={Shotgun assembly of random graphs}, author={Johnston, Tom and Kronenberg, Gal and Roberts, Alexander and Scott, Alex}, journal={arXiv preprint arXiv:2211.14218}, year={2022} }
The rainbow saturation number is linear
Natalie Behague Tom Johnston Shoham Letzter Natasha Morrison Shannon Ogden
SIAM Journal on Discrete Mathematics
2024 38 (2) 1239–1249
@article{behague2024rainbow, title={The rainbow saturation number is linear}, author={Behague, Natalie and Johnston, Tom and Letzter, Shoham and Morrison, Natasha and Ogden, Shannon}, journal = {SIAM Journal on Discrete Mathematics}, volume = {38}, number = {2}, pages = {1239-1249}, year = {2024}, }
Short reachability networks
Carla Groenland Tom Johnston Jamie Radcliffe Alex Scott
Submitted
2022+
@article{groenland2022short, title={Short reachability networks}, author={Groenland, Carla and Johnston, Tom and Radcliffe, Jamie and Scott, Alex}, journal={arXiv preprint arXiv:2208.06630}, year={2022} }
Perfect shuffling with fewer lazy transpositions
Carla Groenland Tom Johnston Jamie Radcliffe Alex Scott
Submitted
2022+
@article{groenland2022perfect, title={Perfect shuffling with fewer lazy transpositions}, author={Groenland, Carla and Johnston, Tom and Radcliffe, Jamie and Scott, Alex}, journal={arXiv preprint arXiv:2208.06629}, year={2022} }
Exact antichain saturation numbers via a generalisation of a result of Lehman-Ron
Paul Bastide Carla Groenland Hugo Jacob Tom Johnston
Combinatorial Theory
2024 4(1)
@article{bastide2024exact, title={Exact antichain saturation numbers via a generalisation of a result of {L}ehman-{R}on}, author={Bastide, Paul and Groenland, Carla and Jacob, Hugo and Johnston, Tom}, journal={Combinatorial Theory}, volume={4}, number={1}, year={2024} }
Improved bounds for 1-independent percolation on \(\mathbb{Z}_n\)
Paul Balister Tom Johnston Michael Savery Alex Scott
Submitted
2022+
@article{balister2022improved, title={Improved bounds for 1-independent percolation on {$\mathbb{Z}_n$}}, author={Balister, Paul and Johnston, Tom and Savery, Michael and Scott, Alex}, year={2022}, journal={arXiv preprint arXiv:2206.12335}, }
Decomposing random permutations into order-isomorphic subpermutations
Carla Groenland Tom Johnston Dániel Korándi Alexander Roberts Alex Scott Jane Tan
SIAM Journal on Discrete Mathematics
2023 37(2) 1252–1261
@article{groenland2022decomposing, title={Decomposing random permutations into order-isomorphic subpermutations}, author={Groenland, Carla and Johnston, Tom and Kor\'andi, D\'aniel and Roberts, Alexander and Scott, Alex and Tan, Jane}, journal = {SIAM Journal on Discrete Mathematics}, volume = {37}, number = {2}, pages = {1252-1261}, year = {2023}, }
The lengths for which bicrucial square-free permutations exist
Carla Groenland Tom Johnston
Enumerative Combinatorics and Applications
2022 2(4) S4PP4
@article{groenland2022lengths, title={The lengths for which bicrucial square-free permutations exist}, author={Groenland, Carla and Johnston, Tom}, journal={Enumerative Combinatorics and Applications}, volume={2}, number={4}, pages={S4PP4}, year={2022}, }
Reconstruction from smaller cards
Carla Groenland Tom Johnston Alex Scott Jane Tan
Submitted
2021+
@article{groenland2021reconstruction, title={Reconstruction from smaller cards}, author={Groenland, Carla and Johnston, Tom and Scott, Alex and Tan, Jane}, journal={arXiv preprint arXiv:2103.13359}, year={2021} }
Reconstructing the degree sequence of a sparse graph from a partial deck
Carla Groenland Tom Johnston Andrey Kupavskii Kitty Meeks Alex Scott Jane Tan
Journal of Combinatorial Theory, Series B
2022 157 283–293
@article{groenland2022reconstructing, title={Reconstructing the degree sequence of a sparse graph from a partial deck}, author={Groenland, Carla and Johnston, Tom and Kupavskii, Andrey and Meeks, Kitty and Scott, Alex and Tan, Jane}, journal = {Journal of Combinatorial Theory, Series B}, volume = {157}, pages = {283-293}, year = {2022}, }
Zero-sum squares in \(\{-1,1\}\)-matrices with low discrepancy
Tom Johnston
Electronic Journal of Combinatorics
2023 30(2) P2.19
@article{johnston2023zero-sum, title={Zero-sum squares in {$\{-1,1\}$}-matrices with low discrepancy}, author={Johnston, Tom}, journal={Electronic Journal of Combinatorics}, volume = {30}, year={2023}, number={2}, pages={P2.19} }
Discrete Mathematics Editors’ Choice List 2022 Discrete Mathematics Editors’ Choice List 2022
Exact hyperplane covers for subsets of the hypercube
James Aaronson Carla Groenland Andrzej Grzesik Tom Johnston Bartłomiej Kielak
Discrete Mathematics
2021 344(9) 112490
@article{aaronson2020exact, title={Exact hyperplane covers for subsets of the hypercube}, author={Aaronson, James and Groenland, Carla and Grzesik, Andrzej and Johnston, Tom and Kielak, Bart{\l}omiej}, journal = {Discrete Mathematics}, year={2021} volume={344}, number={9}, pages={112490}, doi = {https://doi.org/10.1016/j.disc.2021.112490}, }
Cyclically covering subspaces in \(\mathbb{F}_2^n\)
James Aaronson Carla Groenland Tom Johnston
Journal of Combinatorial Theory, Series A
2021 181 105436
@article{aaronson2021cyclically, title={Cyclically covering subspaces in {$\mathbb{F}_2^n$}}, author={Aaronson, James and Groenland, Carla and Johnston, Tom}, journal={Journal of Combinatorial Theory, Series A}, volume={181}, pages={105436}, year={2021}, }
Lipschitz bijections between boolean functions
Tom Johnston Alex Scott
Combinatorics, Probability and Computing
2021 30(4) 513–525
@article{johnston2021lipschitz, title={Lipschitz bijections between boolean functions}, author={Johnston, Tom and Scott, Alex}, journal={Combinatorics, Probability and Computing}, volume={30}, number={4}, pages={513-525}, year={2021}, publisher={Cambridge University Press} }
Intersection sizes of linear subspaces with the hypercube
Carla Groenland Tom Johnston
Journal of Combinatorial Theory, Series A
2020 170 105–142
@article{groenland2020intersection, title={Intersection sizes of linear subspaces with the hypercube}, author={Groenland, Carla and Johnston, Tom}, journal={Journal of Combinatorial Theory, Series A}, volume={170}, pages={105-142}, year={2020}, publisher={Elsevier} }
Exceptional graphs for the random walk
Juhan Aru Carla Groenland Tom Johnston Bhargav Narayanan Alex Roberts
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
2020 56(3) 2017–2027
@article{aru2020exceptional, title={Exceptional graphs for the random walk}, author={Aru, Juhan and Groenland, Carla and Johnston, Tom and Narayanan, Bhargav and Roberts, Alex and Scott, Alex}, journal={Annales de l'Institut Henri Poincar{\'e}, Probabilit{\'e}s et Statistiques}, volume={56}, number={3}, pages={2017--2027}, year={2020}, organization={Institut Henri Poincar{\'e}}, doi = {10.1214/19-AIHP1026} }

Contact

If you have any questions or comments about some interesting maths (or the maths I've done), feel free to send me an email at tom.johnston@bristol.ac.uk.