Tao Jiang

collaborators

6 papers

math.CO2026

Rational exponents near 3/2

Tao Jiang, Sean Longbrake, Liana Yepremyan

Given a graph $H$ , the extremal number $e x (n, H)$ is the maximum number of edges in an $n$ -vertex graph not containing $H$ as a subgraph. The well-known rational exponents conjectur…

math.CO2026

Induced rational exponents near two

Tao Jiang, Sean Longbrake

Given a bipartite graph $H$ and a natural number $s$ , let $ex^{*} (n, H, s)$ denote the maximum number of edges in an $n$ -vertex graph that contains neither $K_{s, s}$ nor an in…

math.CO2026

On the number of families avoiding a subposet

Tao Jiang, Sean Longbrake, Liana Yepremyan

In this paper we show that for any poset $P$ that is not an antichain, the number of induced $P$ -free families in the Boolean lattice $2^{[n]}$ is at most $ 2^{O(\mathrm{La}^*(n,P)…

math.CO2026

On the number of H-free hypergraphs

Tao Jiang, Sean Longbrake

Two central problems in extremal combinatorics are concerned with estimating the number $e x (n, H)$ , the size of the largest $H$ -free hypergraph on $n$ vertices, and the number $forb…

math.CO2025

Tree Posets: Supersaturation, Enumeration, and Randomness

Tao Jiang, Sean Longbrake, Sam Spiro +1

We develop a powerful tool for embedding any tree poset $P$ of height $k$ in the Boolean lattice which allows us to solve several open problems in the area. We show that: * If $H$ …

math.CO2025

Regularization and asymmetric extremal numbers of subdivisions

Tao Jiang, Sean Longbrake

Given a real $I^¼ \geq 1$ , a graph $H$ is $I^¼$ -almost-regular if $I^ (H) \leq I^¼ I^´ (H)$ . The celebrated regularization theorem of ErdÅs and Simonovits states that for every real $0<\va…