8 papers
A reformulation of the discrete Convexity Conjecture via -thresholds
Ruben Ascoli, Xiaoyu He, Jinyoung Park +1
We introduce the notion of "-thresholds'' and show that Talagrand's discrete convexity conjecture is equivalent to the assertion that, for some universal integer , the…
Rational values of the weak saturation limit
Ruben Ascoli, Xiaoyu He
Given a graph , a graph is weakly -saturated if all non-edges of can be added in some order so that each new edge introduces a copy of . The weak saturation number…
Asymptotically half of binary words are shuffle squares
Xiaoyu He, Logan Post
A binary shuffle square is a binary word of even length that can be partitioned into two disjoint, identical subwords. Huang, Nam, Thaper, and the first author conjectured that as…
New Sidorenko-type inequalities in tournaments
Xiaoyu He, Nitya Mani, Jiaxi Nie +2
As a directed analog of Sidorenko's conjecture in extremal graph theory, Fox, Himwich, Zhou, and the second author defined an oriented graph to be tournament Sidorenko (anti-Si…
Ramsey numbers of grid graphs
Xiaoyu He, Ghaura Mahabaduge, Krishna Pothapragada +2
Let the grid graph denote the Cartesian product . For a fixed subgraph of a grid, we study the off-diagonal Ramsey number $\operatorname{gr}(H,…
Polynomial-to-exponential transition in 3-uniform Ramsey numbers
Ruben Ascoli, Xiaoyu He, Hung-Hsun Hans Yu
Let denote the smallest such that any red/blue edge coloring of the complete -uniform hypergraph on vertices contains either red edges among some …