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 polynomial upper bound for poset saturation
Submitted
2023+
@article{bastide2023polynomial,
title={A polynomial upper bound for poset saturation},
author={Bastide, Paul and Groenland, Carla and Ivan, Maria-Romina and Johnston, Tom},
journal={arXiv preprint arXiv:2310.04634},
year={2023}
}
Game connectivity and adaptive dynamics
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
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
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
Submitted
2022+
@article{behague2022rainbow,
title={The rainbow saturation number is linear},
author={Behague, Natalie and Johnston, Tom and Letzter, Shoham and Morrison, Natasha and Ogden, Shannon},
journal={arXiv preprint arXiv:2211.08589},
year={2022}
}
Short reachability networks
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
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
Submitted
2022+
@article{bastide2022exact,
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={arXiv preprint arXiv:2207.07391},
year={2022}
}
Improved bounds for 1-independent percolation on \(\mathbb{Z}_n\)
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
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
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
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
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
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
Exact hyperplane covers for subsets of the hypercube
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 \(\mathbb{F}_2^n\)
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
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
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
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.