My research interests include:

- additive combinatorics
- enumerative combinatorics
- analysis of random discrete structures

### Papers

Research articles published in peer-reviewed journals, in reverse order of acceptance (and not necessarily appearance).

**P6.** (with Jonah Saks) On the homology of several number-theoretic set families. *Enumerative Combinatorics and Applications* **4**,2 (2024), #S2R12, 11 pp. [arXiv]

**P5.** (with Jad Hamdan and Jonah Saks) The lattice of arithmetic progressions. *Australasian Journal of Combinatorics* **84**,3 (2022), 357–374.
[arXiv]

**P4.** (with Luc Devroye and Rosie Y. Zhao) On the peel number and the leaf-height of a Galton-Watson tree. *Combinatorics, Probability and Computing* **32**,1 (2023), 68–90.
[arXiv]

**P3.** (with Anna M. Brandenberger, Luc Devroye, and Rosie Y. Zhao) Leaf multiplicity in a Bienaymé-Galton-Watson tree.
*Discrete Mathematics and Theoretical Computer Science* **24**,1 (2022), #7, 16 pp.
[arXiv]

**P2.** (with Anna M. Brandenberger and Luc Devroye) Root estimation in Galton-Watson trees. *Random Structures and Algorithms* **61**,3 (2022), 520–542.
[arXiv]

**P1.** (with Rosie Y. Zhao) Arithmetic subsequences in a random ordering of an additive set. *Integers: Electronic Journal of Combinatorial Number Theory* **21** (2021),
#A89, 19 pp.
[arXiv]

For recent preprints and unpublished manuscripts, consult the full list of my articles on arXiv, or my Google Scholar profile.

### Reports and theses

Various project and research reports. Some reports were written for internal distribution only, and are therefore not available for download.

**R5.** Structural properties of conditional Galton-Watson trees. M.Sc. thesis, McGill University (Montréal, Québec, August 2022), vi + 75 pp.

**R4.** Finding regularity in Tlingit verb prefixes. Semester project report, McGill University (Montréal, Québec, April 2021), 7 pp.

**R3.** Grid-building algorithms on manifolds. Summer research report, McGill University (Montréal, Québec, August 2020), 10 pp.

**R2.** Typechecking proof scripts: making interactive proof assistants robust. Honours project report, McGill University (Montréal, Québec, December 2019), 10 pp.

**R1.** The OPythn programming language. Software project report, Charles University (Prague, Czech Republic, June 2019), 10 pp.

### Sequences

I contributed the following sequences to the OEIS:

- A360285: Triangle read by rows: $T(n,k)$ is the number of subsets of \(\{1,\ldots,n\}\) of cardinality $k$ in which no two elements are coprime; $n\ge 0$, $0\le k\le \lfloor n/2 \rfloor + [n=1]$.
- A355147: Triangle read by rows: $T(n,k)$ is the number of product-free subsets of \(\{1,\ldots,n\}\) with cardinality $k$; $n\ge 0$, $0\le k\le $A028391($n$).
- A355146: Triangle read by rows: $T(n,k)$ is the number of subsets of \(\{1,\ldots,n\}\) of cardinality $k$ in which every pair of elements if coprime; $n\ge 0$, $0\le k\le $A036234($n$).
- A355145: Triangle read by rows: $T(n,k)$ is the number of primitive subsets of ${1,\ldots,n}$ of cardinality $k$; $n\ge 0$, $0\le k\le \lceil n/2\rceil$.
- A347580: The number of chains of length $k$ in the poset of all arithmetic progressions contained in \(\{1,\ldots,n\}\) of length in the range $[1.\,.n-1]$, ordered by inclusion.
- A341822: The longest known length of a 2-increasing sequence of positive integer triples with entries $\leq n$.
- A339942: Triangle read by rows: $T(n,k)$ is the number of permutations of the cyclic group \({\bf Z}/n{\bf Z}\) whose longest embedded arithmetic progression has length $k$.
- A339941: Triangle read by rows: $T(n,k)$ is the number of permutations of \(\{1,\ldots,n\}\) whose longest embedded arithmetic progression has length $k$.
- A338993: Triangle read by rows: $T(n,k)$ is the number of $k$-permutations of \(\{1,\ldots,n\}\) that form a non-trivial arithmetic progression, $1\leq k\leq n$.
- A338550: The number of binary trees of height $n$ such that the number of nodes at depth $d$ equals $d+1$ for every $d\in {0,\ldots,n}$.
- A335562: The number of unlabelled unary-binary trees with $n$ nodes such that every node with two children has children of different subtree sizes.

### Galton–Watson trees

For my M.Sc., I worked on the probabilistic analysis
of combinatorial objects under the supervision of Luc Devroye. In particular,
we focused our attention on Galton–Watson trees and various structural parameters thereof.
I graduated in August 2022 with a thesis entitled
*Structural properties of conditional Galton-Watson trees*.

### Summer 2020

I received an NSERC Undergraduate Summer Research Award for Summer 2020. I worked with Asa Kohn under the supervision of Michael Lipnowski, designing and implementing sorting algorithms on manifolds with the goal of efficiently building grids on these spaces.

### COMP 400 Honours Project in Computer Science

During the Fall 2019 semester, I undertook a project in the Computation and Logic lab under the supervision of Brigitte Pientka. I worked with Jacob Errington to develop a typechecking algorithm for the Harpoon proof language as well as a translation procedure to convert Harpoon proof scripts into programs in the Beluga programming language. The summary of the work I helped with can be found in the slides to my end-of-term presentation, and my full report is available for download as well.