Sammy Luo

activity

20152025

most citedThe Saxl Conjecture for Fourth Powers via the Semigroup Property

10 citations · 13 across the 18 of their papers we have counts for

collaborators

19 papers

math.CO2025

Iterated sumset expansion in $F_{p}^{n}$

Manik Dhar, Sammy Luo

Given a set $A \subseteq F_{p}^{n}$ , what conditions does one need to guarantee that iterated sumsets of the form $A + \dots + A$ expand quickly (say, within $O (p)$ terms) to the…

math.CO2025

At most 10 cylinders mutually touch: a Ramsey-theoretic approach

Travis Dillon, Junnosuke Koizumi, Sammy Luo

Littlewood asked for the maximum number $N$ of congruent infinite cylinders that can be arranged in $R^{3}$ so that every pair touches. We improve upon the proof of the seco…

math.CO2025

Monochromatic components with many edges in random graphs

Hannah Fox, Sammy Luo

In an $r$ -coloring of edges of the complete graph on $n$ vertices, how many edges are there in the largest monochromatic connected component? A construction of Gyárfás shows that f…

math.CO2024

On off-diagonal $F$ -Ramsey numbers

Sammy Luo, Zixuan Xu

A graph is $(t_{1}, t_{2})$ -Ramsey if any red-blue coloring of its edges contains either a red copy of $K_{t_{1}}$ or a blue copy of $K_{t_{2}}$ . The size Ramsey number is the minimum numb…

math.CO2024

Structure of tight (k,0)-stable graphs

Dingding Dong, Sammy Luo

We say that a graph G is $(k, ℓ)$ -stable if removing $k$ vertices from it reduces its independence number by at most $ℓ$ . We say that G is tight $(k, ℓ)$ -stable if it is $(k…

math.CO2023

A new shift operator-based polynomial method in additive combinatorics

Sammy Luo

We introduce a new form of the polynomial method based on what we call "shift operators," which we use to give efficient and intuitive new proofs of results previously shown using…

math.CO2023

Large monochromatic components in colorings of complete hypergraphs

Lyuben Lichev, Sammy Luo

Gyárfás famously showed that in every $r$ -coloring of the edges of the complete graph $K_{n}$ , there is a monochromatic connected component with at least $\frac{n}{r - 1}$ vertices. A…

math.CO2022

Small subsets with large sumset: Beyond the Cauchy--Davenport bound

Jacob Fox, Sammy Luo, Huy Tuan Pham +1

For a subset $A$ of an abelian group $G$ , given its size $∣ A ∣$ , its doubling $κ = ∣ A + A ∣/∣ A ∣$ , and a parameter $s$ which is small compared to $∣ A ∣$ , we study the size of the largest s…

math.CO2022

On random irregular subgraphs

Jacob Fox, Sammy Luo, Huy Tuan Pham

Let $G$ be a $d$ -regular graph on $n$ vertices. Frieze, Gould, Karoński and Pfender began the study of the following random spanning subgraph model $H = H (G)$ . Assign independently t…

math.CO2022

Monochromatic components with many edges

David Conlon, Sammy Luo, Mykhaylo Tyomkyn

Given an $r$ -edge-coloring of the complete graph $K_{n}$ , what is the largest number of edges in a monochromatic connected component? This natural question has only recently received…

math.CO2021

On connected components with many edges

Sammy Luo

We prove that if $H$ is a subgraph of a complete multipartite graph $G$ , then $H$ contains a connected component $H^{'}$ satisfying $∣ E (H^{'}) ∣∣ E (G) ∣ \geq ∣ E (H) ∣^{2}$ . We use this to prove…

math.CO2021

Multicolor list Ramsey numbers grow exponentially

Jacob Fox, Xiaoyu He, Sammy Luo +1

The list Ramsey number $R_{ℓ} (H, k)$ , recently introduced by Alon, Bucić, Kalvari, Kuperwasser, and Szabó, is a list-coloring variant of the classical Ramsey number. They showed…

math.CO2019

Extremal and Ramsey results on graph blowups

Jacob Fox, Sammy Luo, Yuval Wigderson

Recently, Souza introduced blowup Ramsey numbers as a generalization of bipartite Ramsey numbers. For graphs $G$ and $H$ , say $G ⟶ r H$ if every $r$ -edge-co…

math.CO2019

Generalized Minors and Tensor Invariants

Ian Le, Sammy Luo

Berenstein, Fomin and Zelevinsky defined functions on double Bruhat cells which they called generalized minors. By relating certain double Bruhat cells to configuration spaces of f…

math.CO2017

Stability and exact Turan numbers for matroids

Hong Liu, Sammy Luo, Peter Nelson +1

We consider the Turán-type problem of bounding the size of a set $M \subseteq F_{2}^{n}$ that does not contain a linear copy of a given fixed set $N \subseteq F_{2}^{k}$ ,…

math.NT2017★ 2 cited

Bounded gaps between primes in short intervals

Ryan Alweiss, Sammy Luo

Baker, Harman, and Pintz showed that a weak form of the Prime Number Theorem holds in intervals of the form $[x - x^{0.525}, x]$ for large $x$ . In this paper, we extend a result of Ma…

math.CO2016★ 1 cited

A Counting Lemma for Binary Matroids and Applications to Extremal Problems

Sammy Luo

In graph theory, the Szemerédi regularity lemma gives a decomposition of the indicator function for any graph $G$ into a structured component, a uniform part, and a small error. Th…

math.NT2016

Short Zero-Sum Sequences Over Abelian $p$ -Groups of Large Exponent

Sammy Luo

Let $G$ be a finite abelian group with exponent $n$ . Let $η (G)$ denote the smallest integer $ℓ$ such that every sequence over $G$ of length at least $ℓ$ has a zero-sum subseq…

math.CO2015★ 10 cited

The Saxl Conjecture for Fourth Powers via the Semigroup Property

Sammy Luo, Mark Sellke

The tensor square conjecture states that for $n \geq 10$ , there is an irreducible representation $V$ of the symmetric group $S_{n}$ such that $V \otimes V$ contains every irreducible…

Iterated sumset expansion in Fpn​

At most 10 cylinders mutually touch: a Ramsey-theoretic approach

Monochromatic components with many edges in random graphs

On off-diagonal F-Ramsey numbers

Structure of tight (k,0)-stable graphs

A new shift operator-based polynomial method in additive combinatorics

Large monochromatic components in colorings of complete hypergraphs

Small subsets with large sumset: Beyond the Cauchy--Davenport bound

On random irregular subgraphs

Monochromatic components with many edges

On connected components with many edges

Multicolor list Ramsey numbers grow exponentially

Extremal and Ramsey results on graph blowups

Generalized Minors and Tensor Invariants

Stability and exact Turan numbers for matroids

Bounded gaps between primes in short intervals

A Counting Lemma for Binary Matroids and Applications to Extremal Problems

Short Zero-Sum Sequences Over Abelian p-Groups of Large Exponent

The Saxl Conjecture for Fourth Powers via the Semigroup Property

Iterated sumset expansion in $F_{p}^{n}$

On off-diagonal $F$ -Ramsey numbers

Short Zero-Sum Sequences Over Abelian $p$ -Groups of Large Exponent