Benjamin Gunby

activity

20132024

most citedProof of a conjecture of Guy on class numbers

2 citations · 5 across the 11 of their papers we have counts for

collaborators

13 papers

math.CO2024

When are off-diagonal hypergraph Ramsey numbers polynomial?

David Conlon, Jacob Fox, Benjamin Gunby +5

A natural open problem in Ramsey theory is to determine those $3$ -graphs $H$ for which the off-diagonal Ramsey number $r (H, K_{n}^{(3)})$ grows polynomially with $n$ . We make substan…

math.CO2024

On off-diagonal hypergraph Ramsey numbers

David Conlon, Jacob Fox, Benjamin Gunby +4

A fundamental problem in Ramsey theory is to determine the growth rate in terms of $n$ of the Ramsey number $r (H, K_{n}^{(3)})$ of a fixed $3$ -uniform hypergraph $H$ versus the compl…

math.CO2023

Clique Supersaturation

Quentin Dubroff, Benjamin Gunby, Bhargav Narayanan +1

We study how many copies of a graph $F$ that another graph $G$ with a given number of cliques is guaranteed to have. For example, one of our main results states that for all $t\ge…

math.CO2022

Antichain Codes

Benjamin Gunby, Xiaoyu He, Bhargav Narayanan +1

A family of sets $A$ is said to be an antichain if $x \neq \subset y$ for all distinct $x, y \in A$ , and it is said to be a distance- $r$ code if every pair of distinct elements of $A$ …

math.PR2022

Identifying the Deviator

Noga Alon, Benjamin Gunby, Xiaoyu He +2

A group of players are supposed to follow a prescribed profile of strategies. If they follow this profile, they will reach a given target. We show that if the target is not reached…

math.CO2021

Down-set thresholds

Benjamin Gunby, Xiaoyu He, Bhargav Narayanan

We elucidate the relationship between the threshold and the expectation-threshold of a down-set. Qualitatively, our main result demonstrates that there exist down-sets with polynom…

math.CO2020★ 1 cited

Upper Tails of Subgraph Counts in Sparse Regular Graphs

Benjamin Gunby

What is the probability that a sparse $n$ -vertex random $d$ -regular graph $G_{n}^{d}$ , $n^{1 - c} < d = o (n)$ contains many more copies of a fixed graph $K$ than expected? We determine the b…

math.CO2019

Pattern Avoidance Over a Hypergraph

Maxwell Fishelson, Benjamin Gunby

We consider the problem of bounding the number of permutations $σ \in S_{n}$ that avoid a fixed permutation $π \in S_{k}$ in specific indices given by a $k$ -uniform hypergraph $Λ$ . We ob…

math.CO2017

Asymptotics of Pattern Avoidance in the Klazar Set Partition and Permutation-Tuple Settings

Benjamin Gunby, Dömötör Pálvölgyi

We consider asymptotics of set partition pattern avoidance in the sense of Klazar. Our main result derives the asymptotics of the number of set partitions avoiding a given set part…

math.CO2016★ 1 cited

Asymptotics of Pattern Avoidance in the Permutation-Tuple and Klazar Set Partition Settings

Benjamin Gunby

We consider asymptotics of set partition pattern avoidance in the sense of Klazar. One of the results of this paper extends work of Alweiss, and finds a classification for set part…

math.AG2014

Irreducible Canonical Representations in Positive Characteristic

Benjamin Gunby, Alexander Smith, Allen Yuan

For $X$ a curve over a field of positive characteristic, we investigate when the canonical representation of $Aut (X)$ on $H^{0} (X, Ω_{X})$ is irreducible. Any curve with an irre…

math.NT2014★ 2 cited

Proof of a conjecture of Guy on class numbers

Lynn Chua, Benjamin Gunby, Soohyun Park +1

It is well known that for any prime $p \equiv 3$ (mod $4$ ), the class numbers of the quadratic fields $Q (p)$ and $Q (- p)$ , $h (p)$ and $h (- p)$ respecti…

math.CO2013★ 1 cited

The Dyck pattern poset

Antonio Bernini, Luca Ferrari, Renzo Pinzani +1

We introduce the notion of pattern in the context of lattice paths, and investigate it in the specific case of Dyck paths. Similarly to the case of permutations, the pattern-contai…