Jinyoung Park

activity

20172023

most citedDeep neural network for solving differential equations motivated by Legendre-Galerkin approximation

5 citations · 6 across the 6 of their papers we have counts for

collaborators

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11 papers · 1 filter

math.CO2023

Note on the number of antichains in generalizations of the Boolean lattice

Jinyoung Park, Michail Sarantis, Prasad Tetali

We give a short and self-contained argument that shows that, for any positive integers $t$ and $n$ with $t = O (\frac{n}{l o g n})$ , the number $α ([t]^{n})$ of antichains of t…

math.CO2023

The number of colorings of the middle layers of the Hamming cube

Lina Li, Gweneth McKinley, Jinyoung Park

For an odd integer $n = 2 d - 1$ , let $B_{d}$ be the subgraph of the hypercube $Q_{n}$ induced by the two largest layers. In this paper, we describe the typical structure of prop…

math.CO2021

On a problem of M. Talagrand

Keith Frankston, Jeff Kahn, Jinyoung Park

We address a special case of a conjecture of M. Talagrand relating two notions of "threshold" for an increasing family $F$ of subsets of a finite set $V$ . The full conject…

math.CO2021

Note on the number of balanced independent sets in the Hamming cube

Jinyoung Park

Let $Q_{d}$ be the $d$ -dimensional Hamming cube and $N = ∣ V (Q_{d}) ∣ = 2^{d}$ . An independent set $I$ in $Q_{d}$ is called balanced if $I$ contains the same number of even and odd vertices. We…

math.CO2020

The threshold for the square of a Hamilton cycle

Jeff Kahn, Bhargav Narayanan, Jinyoung Park

Resolving a conjecture of Kühn and Osthus from 2012, we show that $p = 1/ n$ is the threshold for the random graph $G_{n, p}$ to contain the square of a Hamilton cycle.

math.CO2020

Tuza's Conjecture for random graphs

Jeff Kahn, Jinyoung Park

A celebrated conjecture of Zs. Tuza says that in any (finite) graph, the minimum size of a cover of triangles by edges is at most twice the maximum size of a set of edge-disjoint t…

math.CO2019

Thresholds versus fractional expectation-thresholds

Keith Frankston, Jeff Kahn, Bhargav Narayanan +1

Proving a conjecture of Talagrand, a fractional version of the 'expectation-threshold' conjecture of Kalai and the second author, we show for any increasing family $F$ on a finite…

math.CO2019★ 1 cited

The number of maximal independent sets in the Hamming cube

Jeff Kahn, Jinyoung Park

Let $Q_{n}$ be the $n$ -dimensional Hamming cube and $N = 2^{n}$ . We prove that the number of maximal independent sets in $Q_{n}$ is asymptotically \[2n2^{N/4},\] as was conjectured by Ilin…

math.CO2019

An isoperimetric inequality for the Hamming cube and some consequences

Jeff Kahn, Jinyoung Park

Our basic result, an isoperimetric inequality for Hamming cube $Q_{n}$ , can be written: \[ \int h_A^βdμ\ge 2 μ(A)(1-μ(A)). \] Here $μ$ is uniform measure on $V = {0, 1}^{n}$ ( $= V (Q_{n})$ )…

math.CO2018

Stability for maximal independent sets

Jeff Kahn, Jinyoung Park

Answering questions of Y. Rabinovich, we prove "stability" versions of upper bounds on maximal independent set counts in graphs under various restrictions. Roughly these say that b…

math.CO2017

Counting Permutations that Avoid Many Patterns

Yonah Biers-Ariel, Haripriya Chakraborty, John Chiarelli +8

This paper presents a collection of experimental results regarding permutation pattern avoidance, focusing on cases where there are "many" patterns to be avoided.