Publications

My work (mainly) covers extremal combinatorics, finite geometry, spectral graph theory, and coding theory.

My Favorite Publications/Preprints

Here my some of my favorite papers, subjectively ranked. A complete list of all my publications can be found below.

1. The classification of Boolean degree 1 functions in high-dimensional finite vector spaces.
   Proceedings of the American Mathematical Society, Accepted. Preprint.
2. With Hajime Tanaka: The Independence Number of the Orthogonality Graph in Dimension 2^k.
   Combinatorica, 2019. Preprint.
3. With Yuval Filmus: Boolean degree 1 functions on some classical association schemes.
   Journal of Combinatorial Theory A, 2019. Preprint.
4. With Andries E. Brouwer and William M. Kantor: Strongly regular graphs satisfying the 4-vertex condition.
   Combinatorica, 2023. Preprint.
5. With Peter Sin and Qing Xiang: New Bounds for Partial Spreads of H(2d-1, q^2) and Partial Ovoids of the Ree-Tits Octagon.
   Journal of Combinatorial Theory A, 2018. Preprint.
6. With Anurag Bishnoi and Valentina Pepe: A construction for clique-free pseudorandom graphs.
   Combinatorica, 2020. Preprint.

Publications/Preprints Chronologically

Please note that sometimes there are differences between the preprint and the journal version of a paper.

1. A Survey of Cameron-Liebler Sets and Low Degree Boolean Functions in Grassmann Graphs.
   Submitted, Preprint.
2. With John Bamberg, Anurag Bishnoi, Ananthakrishnan Ravi: Ramsey numbers and extremal structures in polar spaces.
   Submitted. Preprint.
3. With Jozefien D'haeseleer, Kai-Uwe Schmidt: A common generalization of hypercube partitions and ovoids in polar spaces.
   Designs, Codes and Cryptography, Accepted. Preprint.
4. The classification of Boolean degree 1 functions in high-dimensional finite vector spaces.
   Proceedings of the American Mathematical Society, Accepted. Preprint.
5. With Morgan Rodgers: Regular Sets of Lines in Rank 3 Polar Spaces.
   Submitted. Preprint.
6. With Paulien Jansen, Linde Lambrecht, Yannick Neyt, Daan Rijpert, Hendrik Van Maldeghem, Magali Victoor:
   Local recognition of the point graphs of some Lie incidence geometries.
   Submitted. Preprint.
7. The strongly regular twisted D_{5,5}(q) graph.
   Discrete Applied Mathematics, 2024. Preprint.
8. On MSR Subspace Families of Lines.
   Advances in Mathematics of Communications, 2023. Preprint.
9. With Yuval Filmus, Edward Hirsch, Sascha Kurz, Artur Riazanov, Alexander Smal, Marc Vinyals: Irreducible subcube partitions.
   Electronic Journal of Combinatorics, 2023. Preprint.
10. With John Bamberg, Yuval Filmus, Sascha Kurz: Affine vector space partitions.
    Designs, Codes and Cryptography, 2023. Preprint.
11. With Stephen P. Glasby and Sam Mattheus: The proportion of non-degenerate complementary subspaces in classical spaces.
    Designs, Codes and Cryptography, 2023. Preprint.
12. Non-Geometric Cospectral Mates of Line Graphs with a Linear Representation.
    Journal of Geometry, 2023. Preprint.
13. With Andries E. Brouwer and William M. Kantor: Strongly regular graphs satisfying the 4-vertex condition.
    Combinatorica, 2023. Preprint.
14. Approximately Strongly Regular Graphs.
    Discrete Mathematics, 2023. Preprint.
15. With Jan De Beule, Jozefien D'haeseleer, Jonathan Mannaert: Degree 2 Boolean Functions on Grassmann Graphs.
    Electronic Journal of Combinatorics, 2023. Preprint.
16. With Sebastian M. Cioabă, Himanshu Gupta, Hirotake Kurihara: The least Euclidean distortion constant of a distance-regular graph.
    Discrete Applied Mathematics, 2022. Preprint.
17. Switching for Small Strongly Regular Graphs.
    Australasian Journal of Combinatorics, 2022. Preprint.
18. With Francesco Pavese and Valentino Smaldore: Graphs cospectral with NU(n+1, q^2), n ≠ 3.
    Discrete Mathematics, 2021. Preprint.
19. With Jozefien D'haeseleer, Jonathan Mannaert, Leo Storme: Cameron-Liebler k-sets in AG(n,q).
    Electronic Journal of Combinatorics, 2021. Preprint.
20. Remarks on the Erdős Matching Conjecture for Vector Spaces.
    European Journal of Combinatorics, 2021. Preprint.
21. With Lilya Budaghyan, Claude Carlet, Diana Davidova, Tor Helleseth, Tim Penttila:
    Relation between o-equivalence and EA-equivalence for Niho bent functions.
    Finite Fields and Their Applications, 2021. Preprint.
22. With Deepak Rajendraprasad and Thilo Weinert: New bounds on the Ramsey number r(I_m, L_n).
    Discrete Mathematics, 2021. Preprint.
23. With Peter J. Dukes and Nathan Lindzey: On the Algebraic Combinatorics of Injections and its Applications to Injection Codes.
    IEEE Transactions on Information Theory, 2020. Preprint.
24. With Peter J. Dukes and Nathan Lindzey: On the Algebraic Combinatorics of Injections (extended abstract).
    Proceedings of the 32nd Conference on Formal Power Series and Algebraic Combinatorics, 2020.
25. With Daniel Heinlein: New and Updated Semidefinite Programming Bounds for Subspace Codes.
    Advances in Mathematics of Communications, 2020. Preprint.
26. With Anurag Bishnoi and Valentina Pepe: A construction for clique-free pseudorandom graphs.
    Combinatorica, 2020. Preprint.
27. With Hajime Tanaka: The Independence Number of the Orthogonality Graph in Dimension 2^k.
    Combinatorica, 2019. Preprint.
28. With Andrey Kupavskii: Regular Intersecting Families.
    Discrete Applied Mathematics, 2019. Preprint.
29. The Chromatic Number of the q-Kneser Graph for large q.
    Electronic Journal of Combinatorics, 2019. Preprint.
30. With Yuval Filmus: Boolean constant degree functions on the slice are juntas.
    Discrete Mathematics, 2019. Preprint.
31. With Yuval Filmus: Boolean degree 1 functions on some classical association schemes.
    Journal of Combinatorial Theory A, 2019. Preprint.
32. With Akihiro Munemasa: New Strongly Regular Graphs from Finite Geometries via Switching.
    Linear Algebra and Its Applications, 2019. Preprint.
33. With Mohammad Adm, Ryan Bergen, Sam Jaques, Karen Meagher, Alison Purdy, Boting Yang:
    Ovoids of Generalized Quadrangles of Order (q,q^2−q) and Delsarte Cocliques in Related Strongly Regular Graphs.
    Journal of Combinatorial Designs, 2018. Preprint.
34. With Peter Sin and Qing Xiang: New Bounds for Partial Spreads of H(2d-1, q^2) and Partial Ovoids of the Ree-Tits Octagon.
    Journal of Combinatorial Theory A, 2018. Preprint.
35. With Klaus Metsch and Bernhard Mühlherr: An EKR theorem for finite buildings of type Dl.
    Journal of Algebraic Combinatorics, 2018.
36. With Karen Meagher: Manickam-Miklós-Singhi Conjectures on Partial Geometries.
    Designs, Codes and Cryptography, 2018. Preprint.
37. With Klaus Metsch: Large {0, 1,...,t}-Cliques in Dual Polar Graphs.
    Journal of Combinatorial Theory A, 2018. Preprint.
38. With Andries E. Brouwer, Sebastian M. Cioabă, and Matt McGinnis:
    The smallest eigenvalues of Hamming graphs, Johnson graphs and other distance-regular graphs with classical parameters.
    Journal of Combinatorial Theory B, 2018. Preprint.
39. With Ryan Bergen, Shaun Fallat, Adam Gorr, Karen Meagher, Alison Purdy, Boting Yang, Guanglong Yu: Infection in Hypergraphs.
    Discrete Applied Mathematics, 2018. Preprint.
40. With Anurag Bishnoi: The non-existence of distance-2 ovoids in H(4)^D.
    Contributions to Discrete Mathematics, 2017. Preprint.
41. With John Bamberg and Jan De Beule: New non-existence proofs for ovoids of Hermitian polar spaces and hyperbolic quadrics.
    Annals of Combinatorics, 2017. Preprint.
42. A Switching for Strongly Regular Collinearity Graphs From Polar Spaces.
    Journal of Algebraic Combinatorics, 2017. Preprint.
43. A Note on the Manickam-Miklós-Singhi Conjecture for Vector Spaces.
    European Journal of Combinatorics, 2016. Preprint.
44. Cross-intersecting Erdős-Ko-Rado Sets in Dual Polar Graphs.
    Electronic Journal of Combinatorics, 2015.
45. A new upper bound for constant distance codes of generators on hermitian polar spaces of type H(2d − 1, q^2).
    Journal of Geometry, 2014. Preprint.
46. With Klaus Metsch: On the Maximum Size of Erdős-Ko-Rado Sets in H(2d+1, q^2).
    Designs, Codes and Cryptography, 2014. Preprint.
47. A Characterisation of the Natural Embedding of the Split Cayley Hexagon in PG(6,q) by Intersection Numbers in Finite Projective Spaces of Arbitrary Dimension.
    Discrete Mathematics, 2014. Preprint.

Unpublished/Unrefereed Reports

1. Ratio bound (Lovasz number) vs inertia bound, Unpublished Note, 2023.
2. With Gary Greaves, Franklin Kenter, Brendan Rooney: Answer to IMAGE Problem 67-1, Answer, 2022.
3. Partial m-Spreads of Hermitian Polar Spaces, Report, 2022.
4. With Jacques Verstraëte: Large (k; r, s; n, q)-sets in Projective Spaces.
   2022. Preprint.
5. Two Small Improvements on Ramsey Numbers, 2020.
6. Report on the GM-Switching Class of Sp(6, 2), 2020. Superseded by: Switching for Small Strongly Regular Graphs.

Coauthors

Yuval Filmus (4), John Bamberg (3), Anurag Bishnoi (3), Jozefien D'haeseleer (3), Karen Meagher (3), Klaus Metsch (3), Ryan Bergen (2), Andries E. Brouwer (2), Sebastian M. Cioabă (2), Jan De Beule (2), Sascha Kurz (2), Jonathan Mannaert (2), Alison Purdy (2), Boting Yang (2), Mohammad Adm, Lilya Budaghyan, Claude Carlet, Diana Davidova, Peter J. Dukes, Shaun Fallat, Stephen P. Glasby, Adam Gorr, Himanshu Gupta, Daniel Heinlein, Tor Helleseth, Edward Hirsch, Paulien Jansen, Sam Jaques, William M. Kantor, Andrey Kupavskii, Hirotake Kurihara, Linde Lambrecht, Nathan Lindzey, Matt McGinnis, Sam Mattheus, Bernhard Mühlherr, Akihiro Munemasa, Yannick Neyt, Francesco Pavese, Tim Penttila, Valentina Pepe, Deepak Rajendraprasad, Ananthakrishnan Ravi, Artur Riazanov, Daan Rijpert, Morgan Rodgers, Kai-Uwe Schmidt, Peter Sin, Alexander Smal, Valentino Smaldore, Leo Storme, Hajime Tanaka, Hendrik Van Maldeghem, Magali Victoor, Marc Vinyals, Thilo Weinert, Qing Xiang, Guanglong Yu.

Theses

• PhD Thesis (English), Algebraic Combinatorics Intersecting Finite Geometry, 2015.
• Master Thesis (German), Intriguing Sets in Polar Spaces, 2011.
• Bachelor Thesis (German), $1 \equiv p$ Results in Finite Projective Spaces, 2009.