Matthew Kwan

collaborators

6 papers

math.CO2026

No- $(k + 1)$ -in-line problem for $k ⩾ 3$

Anubhab Ghosal, Ritesh Goenka, Alexandr Grebennikov +3

What is the maximum number of points one can place in an $n \times n$ grid such that every Euclidean line contains at most $k$ points? For $k = 2$ , this is the notorious no-three-i…

math.CO2026

Permanents of random matrices over finite fields

Zach Hunter, Matthew Kwan, Lisa Sauermann

Fix a finite field $F_{q}$ and let $A \in F_{q}^{n \times n}$ be a uniformly random $n \times n$ matrix over $F_{q}$ . The asymptotic distribution of the determinant…

math.CO2025

Counting Perfect Matchings In Dirac Hypergraphs

Matthew Kwan, Roodabeh Safavi, Yiting Wang

One of the foundational theorems of extremal graph theory is Dirac's theorem, which says that if an n-vertex graph G has minimum degree at least n/2, then G has a Hamilton cycle, a…

math.PR2025

Exponential anticoncentration of the permanent

Zach Hunter, Matthew Kwan, Lisa Sauermann

Let $A \in R^{n \times n}$ be a random matrix with independent entries, and suppose that the entries are "uniformly anticoncentrated" in the sense that there is a constant $\…

math.CO2025

Geometric Littlewood-Offord problems via lattice point counting

Alexandr Grebennikov, Matthew Kwan

Consider nonzero vectors $a_{1}, \dots, a_{n} \in C^{k}$ , independent Rademacher random variables $I^¾_{1}, \dots, I^¾_{n}$ , and a set $S \subseteq C^{k}$ . What upper bound…

math.CO2025

Algebraic aspects of the polynomial Littlewood-Offord problem

Zhihan Jin, Matthew Kwan, Lisa Sauermann +1

Consider a degree- $d$ polynomial $f (I^¾_{1}, \dots, I^¾_{n})$ of independent Rademacher random variables $I^¾_{1}, \dots, I^¾_{n}$ . To what extent can $f (I^¾_{1}, \dots, I^¾_{n})$ concentrate on a single…

No-(k+1)-in-line problem for k⩾3

Permanents of random matrices over finite fields

Counting Perfect Matchings In Dirac Hypergraphs

Exponential anticoncentration of the permanent

Geometric Littlewood-Offord problems via lattice point counting

Algebraic aspects of the polynomial Littlewood-Offord problem

No- $(k + 1)$ -in-line problem for $k ⩾ 3$