Daniel G. Zhu

activity

20242026

most citedAn improved lower bound on the Shannon capacities of complements of odd cycles

1 citations · 1 across the 12 of their papers we have counts for

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5 papers · 1 filter

math.PR2024

Local limit theorem for joint subgraph counts

Ashwin Sah, Mehtaab Sawhney, Daniel G. Zhu

Extending a previous result of the first two authors, we prove a local limit theorem for the joint distribution of subgraph counts in the Erdős-Rényi random graph $G (n, p)$ . This li…

math.CO2024

Uniform stability of ranks

Guy Moshkovitz, Daniel G. Zhu

Chen and Ye recently proved that the analytic rank of tensors is stable under field extensions, assuming a fixed base field. Using a more careful analysis, we show that this assump…

math.CO2024

Maximum shattering

Noga Alon, Varun Sivashankar, Daniel G. Zhu

A family $F$ of subsets of $[n] = {1, 2, \dots, n}$ shatters a set $A \subseteq [n]$ if for every $A^{'} \subseteq A$ there is an $F \in F$ such that $F \cap A = A^{'}$ .…

math.NT2024

A correction to a result of Chinburg and Henriksen on powers of integer polynomials

Daniel G. Zhu

For a positive integer $k$ , let $m (k)$ be the minimum positive integer $m$ such that $m x$ can be written as an integer linear combination of $k$ th powers of integer polynomials. We…

math.CO2024★ 1 cited

An improved lower bound on the Shannon capacities of complements of odd cycles

Daniel G. Zhu

Improving a 2003 result of Bohman and Holzman, we show that for $n \geq 1$ , the Shannon capacity of the complement of the $2 n + 1$ -cycle is at least $(2^{r_n} + 1)^{1/r_n} = 2 + Ω(2^…