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

collaborators

12 papers

math.CO2026

The Minkowski grid has robustly many repeated distances

Sungchul Lee, Cosmin Pohoata, Daniel G. Zhu

We show that there exists a constant $δ > 0$ such that for any positive integer $n$ there exists a set of $n$ points $P \subset R^{2}$ with the following property: for every…

cs.GT2026

Deterministic Metric Distortion of Top-2 Voting

Alec Sun, Daniel Zhu

We give tight bounds on the metric distortion of top-2 deterministic voting mechanisms. We first exploit the restrictive structure of top-2 voting to reduce the space of worst-case…

math.CO2026

Schur complements for tensors and multilinear commutative rank

Guy Moshkovitz, Daniel G. Zhu

We show that three notions of rank for matrices of multilinear forms are equivalent. This result generalizes a classical result of Flanders, corrects a minor hole in work of Fortin…

math.CO2026

A Halász-type theorem for permutation anticoncentration

Zach Hunter, Cosmin Pohoata, Daniel G. Zhu

Given a set $A = {a_{1}, \dots, a_{n}}$ of real numbers and real coefficients $b_{1}, \dots, b_{n}$ , consider the distribution of the sum obtained by pairing the $a_{i}$ 's with the $b_{i}$ 's acc…

math.CO2025

A Lovász-Kneser theorem for triangulations

Anton Molnar, Cosmin Pohoata, Michael Zheng +1

We show that the Kneser graph of triangulations of a convex $n$ -gon has chromatic number $n - 2$ .

math.CO2025

Hypergraphic zonotopes and acyclohedra

Cosmin Pohoata, Daniel G. Zhu

We introduce a higher-uniformity analogue of graphic zonotopes and permutohedra. Specifically, given a $(d + 1)$ -uniform hypergraph $H$ , we define its hypergraphic zonotope $\mathcal…

math.CO2025

Series-parallel graphs and hypercube degeneracy

Daniel G. Zhu

Several recent works have identified patterns that must exist in dense subsets of either the vertices or the edges of a large hypercube. We introduce a framework, based on the conc…

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^…