Jonathan Tidor

activity

20132026

most citedEquiangular lines with a fixed angle

65 citations · 108 across the 25 of their papers we have counts for

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22 papers · 1 filter

math.CO2026

The Erdős distinct distances problem in $R^{3}$

Jonathan Tidor, Hung-Hsun Hans Yu, Dmitrii Zakharov

We prove that $N$ points in $R^{3}$ determine at least $N^{2/3 - o (1)}$ distinct distances.

math.CO2026

$K_{2, t + 1}$ -free graphs with many copies of $K_{t, t}$

Cosmin Pohoata, Jonathan Tidor, Hung-Hsun Hans Yu

For every fixed integer $t \geq 3$ , we construct an $n$ -vertex $K_{2, t + 1}$ -free graph containing $Ω_{t} (n^{2})$ copies of $K_{t, t}$ . Combined with a simple counting argument, this shows…

math.CO2024

On monochromatic solutions to linear equations over the integers

Dingding Dong, Nitya Mani, Huy Tuan Pham +1

We study the number of monochromatic solutions to linear equations in a $2$ -coloring of ${1, \dots, n}$ . We show that any nontrivial linear equation has a constant fraction of sol…

math.CO2024

More unit distances in arbitrary norms

Josef Greilhuber, Carl Schildkraut, Jonathan Tidor

For $d \geq 2$ and any norm on $R^{d}$ , we prove that there exists a set of $n$ points that spans at least $(\frac{d}{2} - o (1)) n lo g_{2} n$ unit distances under this norm for every…

math.CO2024

Multilevel polynomial partitioning and semialgebraic hypergraphs: regularity, Turán, and Zarankiewicz results

Jonathan Tidor, Hung-Hsun Hans Yu

We prove three main results about semialgebraic hypergraphs. First, we prove an optimal and oblivious regularity lemma. Fox, Pach, and Suk proved that the class of $k$ -uniform semi…

math.CO2023

Ramsey and Turán numbers of sparse hypergraphs

Jacob Fox, Maya Sankar, Michael Simkin +2

Degeneracy plays an important role in understanding Turán- and Ramsey-type properties of graphs. Unfortunately, the usual hypergraphical generalization of degeneracy fails to captu…

math.CO2023★ 1 cited

Triangle Ramsey numbers of complete graphs

Jacob Fox, Jonathan Tidor, Shengtong Zhang

A graph is $H$ -Ramsey if every two-coloring of its edges contains a monochromatic copy of $H$ . Define the $F$ -Ramsey number of $H$ , denoted by $r_{F} (H)$ , to be the minimum number of…

math.CO2023

Uniform sets with few progressions via colorings

Mingyang Deng, Jonathan Tidor, Yufei Zhao

Ruzsa asked whether there exist Fourier-uniform subsets of $Z / N Z$ with density $α$ and 4-term arithmetic progression (4-AP) density at most $α^{C}$ , for arbitrarily l…

math.CO2021

Quantitative bounds for the $U^{4}$ -inverse theorem over low characteristic finite fields

Jonathan Tidor

This paper gives the first quantitative bounds for the inverse theorem for the Gowers $U^{4}$ -norm over $F_{p}^{n}$ when $p = 2, 3$ . We build upon earlier work of Gowers and Miliće…

math.CO2021★ 3 cited

Non-classical polynomials and the inverse theorem

Aaron Berger, Ashwin Sah, Mehtaab Sawhney +1

In this note we characterize when non-classical polynomials are necessary in the inverse theorem for the Gowers $U^{k}$ -norm. We give a brief deduction of the fact that a bounded fun…

math.CO2021★ 11 cited

Popular differences for matrix patterns

Aaron Berger, Ashwin Sah, Mehtaab Sawhney +1

The following combinatorial conjecture arises naturally from recent ergodic-theoretic work of Ackelsberg, Bergelson, and Best. Let $M_{1}$ , $M_{2}$ be $k \times k$ integer matrices, $G$ …

math.CO2020★ 2 cited

Joints of varieties

Jonathan Tidor, Hung-Hsun Hans Yu, Yufei Zhao

We generalize the Guth--Katz joints theorem from lines to varieties. A special case says that $N$ planes (2-flats) in 6 dimensions (over any field) have $O (N^{3/2})$ joints, where…

math.CO2020★ 9 cited

Spherical two-distance sets and eigenvalues of signed graphs

Zilin Jiang, Jonathan Tidor, Yuan Yao +2

We study the problem of determining the maximum size of a spherical two-distance set with two fixed angles (one acute and one obtuse) in high dimensions. Let $N_{α, β} (d)$ denote th…

math.CO2020

A counterexample to the Bollobás-Riordan conjectures on sparse graph limits

Ashwin Sah, Mehtaab Sawhney, Jonathan Tidor +1

Bollobás and Riordan, in their paper "Metrics for sparse graphs," proposed a number of provocative conjectures extending central results of quasirandom graphs and graph limits to s…

math.CO2019★ 3 cited

Induced arithmetic removal: complexity 1 patterns over finite fields

Jacob Fox, Jonathan Tidor, Yufei Zhao

We prove an arithmetic analog of the induced graph removal lemma for complexity 1 patterns over finite fields. Informally speaking, we show that given a fixed collection of $r$ -col…

math.CO2019★ 3 cited

Testing linear-invariant properties

Jonathan Tidor, Yufei Zhao

Fix a prime $p$ and a positive integer $R$ . We study the property testing of functions $F_{p}^{n} \to [R]$ . We say that a property is testable if there exists an oblivious tester…

math.CO2019★ 65 cited

Equiangular lines with a fixed angle

Zilin Jiang, Jonathan Tidor, Yuan Yao +2

Solving a longstanding problem on equiangular lines, we determine, for each given fixed angle and in all sufficiently large dimensions, the maximum number of lines pairwise separat…

math.CO2018★ 2 cited

Hypergraph expanders of all uniformities from Cayley graphs

David Conlon, Jonathan Tidor, Yufei Zhao

Hypergraph expanders are hypergraphs with surprising, non-intuitive expansion properties. In a recent paper, the first author gave a simple construction, which can be randomized, o…

math.CO2016★ 1 cited

1-color-avoiding paths, special tournaments, and incidence geometry

Jonathan Tidor, Victor Y. Wang, Ben Yang

We discuss two approaches to a recent question of Loh: must a 3-colored transitive tournament on $N$ vertices have a 1-color-\emph{avoiding} path of vertex-length at least $N^{2/3}…

math.CO2015★ 6 cited

Dense binary $P G (t - 1, 2)$ -free matroids have critical number $t - 1$ or $t$

Jonathan Tidor

The critical threshold of a (simple binary) matroid $N$ is the infimum over all $ρ$ such that any $N$ -free matroid $M$ with $∣ M ∣ > ρ 2^{r (M)}$ has bounded critical number. In this…

math.CO2015

Two classes of modular $p$ -Stanley sequences

Mehtaab Sawhney, Jonathan Tidor

Consider a set $A$ with no $p$ -term arithmetic progressions for $p$ prime. The $p$ -Stanley sequence of a set $A$ is generated by greedily adding successive integers that do not cre…

math.CO2013★ 1 cited

Convex geometric (k+2)-quasiplanar representations of semi-bar k-visibility graphs

Jesse Geneson, Tanya Khovanova, Jonathan Tidor

We examine semi-bar visibility graphs in the plane and on a cylinder in which sightlines can pass through k objects. We show every semi-bar k-visibility graph has a (k+2)-quasiplan…

The Erdős distinct distances problem in R3

K2,t+1​-free graphs with many copies of Kt,t​

On monochromatic solutions to linear equations over the integers

More unit distances in arbitrary norms

Multilevel polynomial partitioning and semialgebraic hypergraphs: regularity, Turán, and Zarankiewicz results

Ramsey and Turán numbers of sparse hypergraphs

Triangle Ramsey numbers of complete graphs

Uniform sets with few progressions via colorings

Quantitative bounds for the U4-inverse theorem over low characteristic finite fields

Non-classical polynomials and the inverse theorem

Popular differences for matrix patterns

Joints of varieties

Spherical two-distance sets and eigenvalues of signed graphs

A counterexample to the Bollobás-Riordan conjectures on sparse graph limits

Induced arithmetic removal: complexity 1 patterns over finite fields

Testing linear-invariant properties

Equiangular lines with a fixed angle

Hypergraph expanders of all uniformities from Cayley graphs

1-color-avoiding paths, special tournaments, and incidence geometry

Dense binary PG(t−1,2)-free matroids have critical number t−1 or t

Two classes of modular p-Stanley sequences

Convex geometric (k+2)-quasiplanar representations of semi-bar k-visibility graphs

The Erdős distinct distances problem in $R^{3}$

$K_{2, t + 1}$ -free graphs with many copies of $K_{t, t}$

Quantitative bounds for the $U^{4}$ -inverse theorem over low characteristic finite fields

Dense binary $P G (t - 1, 2)$ -free matroids have critical number $t - 1$ or $t$

Two classes of modular $p$ -Stanley sequences