# Research

I am currently pursuing an M.Sc. in Mathematics, working on the probabilistic analysis of combinatorial objects under the supervision of Luc Devroye. My research interests include:

• probabilistic analysis of algorithms
• analysis of random discrete structures
• enumerative combinatorics

### Papers

P2. (with Anna M. Brandenberger and Luc Devroye) Root estimation in Galton-Watson trees. To appear in Random Structures and Algorithms, 24 pp. [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]

### Submitted papers

Papers submitted for publication in refereed journals.

☀ (with Luc Devroye and Rosie Y. Zhao) The independence number of a Bienaymé-Galton-Watson tree and related parameters. arXiv preprint 2106.14389, 20 pp.
☀ (with Jad Hamdan and Jonah Saks) The lattice of arithmetic progressions. arXiv preprint 2106.05949, 15 pp.
☀ (with Anna M. Brandenberger, Luc Devroye, and Rosie Y. Zhao) Leaf multiplicity in a Bienaymé-Galton-Watson tree. arXiv preprint 2105.12046, 11 pp.

### Reports

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

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:

• 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.

### 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.