Tom Johnston

About

I'm currently working towards a DPhil in combinatorics at the University of Oxford under the supervision of Alex Scott. Before starting my DPhil in 2017 I did an MMath in Oxford.

My main research interest is extremal combinatorics, and I tend to spend most of my time working on problems that involve hypercubes in some way.

Papers

Download the PDF of Reconstructing trees from small cards
Reconstructing trees from small cards
Carla Groenland Tom Johnston Alex Scott Jane Tan
Submitted
2021+
@article{groenland2021reconstructingtrees, title={Reconstructing trees from small cards}, author={Groenland, Carla and Johnston, Tom and Scott, Alex and Tan, Jane}, journal={arXiv preprint arXiv:2103.13359}, year={2021} }
Download the PDF of Reconstructing the degree sequence of a sparse graph from a partial deck
Reconstructing the degree sequence of a sparse graph from a partial deck
Carla Groenland Tom Johnston Andrey Kupavskii Kitty Meeks Alex Scott Jane Tan
Submitted
2021+
@article{groenland2021reconstructing, 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={arXiv preprint arXiv:2102.08679}, year={2021} }
Download the PDF of Zero-sum squares in \(\{-1,1\}\)-matrices with low discrepancy Download the code for Zero-sum squares in \(\{-1,1\}\)-matrices with low discrepancy
Zero-sum squares in \(\{-1,1\}\)-matrices with low discrepancy
Tom Johnston
Submitted
2020+
@article{johnston2020zero-sum, title={Zero-sum squares in {$\{-1,1\}$}-matrices with low discrepancy}, author={Johnston, Tom}, journal={arXiv preprint arXiv:2010.10310}, year={2020} }
Download the PDF of Exact hyperplane covers for subsets of the hypercube Download the code for Exact hyperplane covers for subsets of the hypercube
Exact hyperplane covers for subsets of the hypercube
James Aaronson Carla Groenland Andrzej Grzesik Tom Johnston Bartłomiej Kielak
Submitted
2020+
@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={arXiv preprint arXiv:2010.00315}, year={2020} }
Download the PDF of Cyclically covering subspaces in \(\mathbb{F}_2^n\) Digital Object Identifier
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}, }
Download the PDF of Lipschitz bijections between boolean functions Digital Object Identifier
Lipschitz bijections between boolean functions
Tom Johnston Alex Scott
Combinatorics, Probability and Computing
2020 1–13
@article{johnstonlipschitz, title={Lipschitz bijections between boolean functions}, author={Johnston, Tom and Scott, Alex}, journal={Combinatorics, Probability and Computing}, pages={1--13}, publisher={Cambridge University Press} }
Download the PDF of Intersection sizes of linear subspaces with the hypercube Download the code for Intersection sizes of linear subspaces with the hypercube Digital Object Identifier
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} }
Download the PDF of Exceptional graphs for the random walk Digital Object Identifier
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 thomas.johnston@lmh.ox.ac.uk.