Vishesh Jain

activity

20132023

most citedSingularity of random symmetric matrices -- a combinatorial approach to improved bounds

25 citations · 70 across the 30 of their papers we have counts for

collaborators

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10 papers · 1 filter

math.CO2023

The binomial random graph is a bad inducer

Vishesh Jain, Marcus Michelen, Fan Wei

For a finite graph $F$ and a value $p \in [0, 1]$ , let $I (F, p)$ denote the largest $y$ for which there is a sequence of graphs of edge density approaching $p$ so that the induced $F…

math.CO2022★ 1 cited

Optimal thresholds for Latin squares, Steiner Triple Systems, and edge colorings

Vishesh Jain, Huy Tuan Pham

We show that the threshold for the binomial random $3$ -partite, $3$ -uniform hypergraph $G^{3} ((n, n, n), p)$ to contain a Latin square is $Θ (lo g n / n)$ . We also prove analogous resul…

math.CO2021

Anticoncentration versus the number of subset sums

Vishesh Jain, Ashwin Sah, Mehtaab Sawhney

Let $w = (w_{1}, \dots, w_{n}) \in R^{n}$ . We show that for any $n^{- 2} \leq ε \leq 1$ , if \[\#\{\vecξ \in \{0,1\}^{n}: \langle \vecξ, \vec{w} \rangle = τ\} \ge 2^{-εn}\cdot 2…

math.CO2020★ 1 cited

The probability of selecting $k$ edge-disjoint Hamilton cycles in the complete graph

Asaf Ferber, Kaarel Haenni, Vishesh Jain

Let $H_{1}, \dots, H_{k}$ be Hamilton cycles in $K_{n}$ , chosen independently and uniformly at random. We show, for $k = o (n^{1/100})$ , that the probability of $H_{1}, \dots, H_{k}$ being edge-d…

math.CO2019

On the counting problem in inverse Littlewood--Offord theory

Asaf Ferber, Vishesh Jain, Kyle Luh +1

Let $ε_{1}, \dots, ε_{n}$ be i.i.d. Rademacher random variables taking values $\pm 1$ with probability $1/2$ each. Given an integer vector $a = (a_{1}, \dots, a_{n})$ , its c…

math.CO2019★ 3 cited

Uniformity-independent minimum degree conditions for perfect matchings in hypergraphs

Asaf Ferber, Vishesh Jain

In this note, we prove that there exists a universal constant $c = \frac{43}{50}$ such that for every $k \in N$ and every $d < k /2$ , every $k$ -uniform hypergraph on $n$ vertice…

math.CO2018

Towards the linear arboricity conjecture

Asaf Ferber, Jacob Fox, Vishesh Jain

The linear arboricity of a graph $G$ , denoted by $la (G)$ , is the minimum number of edge-disjoint linear forests (i.e. forests in which every connected component is a path) i…

math.CO2018

On the k-planar local crossing number

John Asplund, Thao do, Arran Hamm +1

Given a fixed positive integer $k$ , the $k$ -planar local crossing number of a graph $G$ , denoted by $LCR_{k} (G)$ , is the minimum positive integer $L$ such that $G$ can be deco…

math.CO2018

1-factorizations of pseudorandom graphs

Asaf Ferber, Vishesh Jain

A $1$ -factorization of a graph $G$ is a collection of edge-disjoint perfect matchings whose union is $E (G)$ . A trivial necessary condition for $G$ to admit a $1$ -factorization is t…

math.CO2018

Number of 1-factorizations of regular high-degree graphs

Asaf Ferber, Vishesh Jain, Benny Sudakov

A $1$ -factor in an $n$ -vertex graph $G$ is a collection of $\frac{n}{2}$ vertex-disjoint edges and a $1$ -factorization of $G$ is a partition of its edges into edge-disjoint $1$ -fac…

The binomial random graph is a bad inducer

Optimal thresholds for Latin squares, Steiner Triple Systems, and edge colorings

Anticoncentration versus the number of subset sums

The probability of selecting k edge-disjoint Hamilton cycles in the complete graph

On the counting problem in inverse Littlewood--Offord theory

Uniformity-independent minimum degree conditions for perfect matchings in hypergraphs

Towards the linear arboricity conjecture

On the k-planar local crossing number

1-factorizations of pseudorandom graphs

Number of 1-factorizations of regular high-degree graphs

The probability of selecting $k$ edge-disjoint Hamilton cycles in the complete graph