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20242026
most citedThe Frankl-Pach upper bound is not tight for any uniformity

1 citations · 1 across the 1 of their papers we have counts for

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4 papers

math.CO2026★ 1 cited

The Frankl-Pach upper bound is not tight for any uniformity

Gennian Ge, Zixiang Xu, Chi Hoi Yip +2

For any positive integers , what is the maximum size of a -uniform set system in with VC-dimension at most ? In 1984, Frankl and Pach initiated the s…

math.CO2025

Largest -uniform set systems with VC-dimension

Jian Wang, Zixiang Xu, Shengtong Zhang

We determine the largest size of -uniform set systems on with VC-dimension for all .

math.CO2025

Uniform set systems with small VC-dimension

Ting-Wei Chao, Zixiang Xu, Chi Hoi Yip +1

We investigate the longstanding problem of determining the maximum size of a -uniform set system with VC-dimension at most . Since the seminal 1984 work of Frankl and Pac…

math.CO2024

Conic programming to understand sums of squares of eigenvalues of graphs

Gabriel Coutinho, Thomás Jung Spier, Shengtong Zhang

In this paper we prove a conjecture by Wocjan, Elphick and Anekstein (2018) which upper bounds the sum of the squares of the positive (or negative) eigenvalues of the adjacency mat…