Matthew Kwan

activity

20232026

most citedResolution of the quadratic Littlewood--Offord problem

2 citations · 2 across the 8 of their papers we have counts for

collaborators

9 papers

math.CO2026

Nonlinear lower-tail large deviations at criticality

Matthew Kwan, Huy Tuan Pham

We introduce general methods to derive lower tail large deviation principles, for a variety of nonlinear problems of combinatorial interest. These methods are especially effective…

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.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 $ξ_{1}, \dots, ξ_{n}$ , and a set $S \subseteq C^{k}$ . What upper bounds…

math.CO2025

Algebraic aspects of the polynomial Littlewood-Offord problem

Zhihan Jin, Matthew Kwan, Lisa Sauermann +1

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

math.CO2024

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.CO2023★ 2 cited

Resolution of the quadratic Littlewood--Offord problem

Matthew Kwan, Lisa Sauermann

Consider a quadratic polynomial $Q (ξ_{1}, \dots, ξ_{n})$ of independent Rademacher random variables $ξ_{1}, \dots, ξ_{n}$ . To what extent can $Q (ξ_{1}, \dots, ξ_{n})$ concentrate on a si…

math.CO2023

Exponentially many graphs are determined by their spectrum

Illya Koval, Matthew Kwan

As a discrete analogue of Kac's celebrated question on "hearing the shape of a drum", and towards a practical graph isomorphism test, it is of interest to understand which graphs a…

Nonlinear lower-tail large deviations at criticality

No-(k+1)-in-line problem for k⩾3

Permanents of random matrices over finite fields

Exponential anticoncentration of the permanent

Geometric Littlewood-Offord problems via lattice point counting

Algebraic aspects of the polynomial Littlewood-Offord problem

Counting Perfect Matchings In Dirac Hypergraphs

Resolution of the quadratic Littlewood--Offord problem

Exponentially many graphs are determined by their spectrum

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