Shengtong Zhang

activity

20192026

most citedEquiangular lines with a fixed angle

65 citations · 89 across the 16 of their papers we have counts for

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10 papers · 1 filter

math.CO2023★ 2 cited

Hypergraph independence polynomials with a zero close to the origin

Shengtong Zhang

For each uniformity $k \geq 3$ , we construct $k$ -uniform linear hypergraphs $G$ with arbitrarily large maximum degree $Δ$ whose independence polynomial $Z_{G}$ has a root $λ$ with $\…

math.CO2023

A Short Proof to Defant and Kravitz's theorem on the Length of Hitomezashi Loops

Qiuyu Ren, Shengtong Zhang

We provide a shorter proof to Defant and Kravitz's theorem (arXiv:2201.03461, Theorem 1.2) on the length of Hitomezashi loops modulo 8.

math.CO2022

Log-Concavity in Powers of Infinite Series Close to $(1 - z)^{- 1}$

Shengtong Zhang

In this paper, we use the analytic method of Odlyzko and Richmond to study the log-concavity of power series. If $f (z) = \sum_{n} a_{n} z^{n}$ is an infinite series with $a_{n} \geq 1$ and…

math.CO2021

Domination polynomial is unimodal for large graphs with a universal vertex

Shengtong Zhang

For a undirected simple graph $G$ , let $d_{i} (G)$ be the number of $i$ -element dominating vertex set of $G$ . The domination polynomial of the graph $G$ is defined as $$D(G, x) = \sum…

math.CO2021

Note on the Turán number of the $3$ -linear hypergraph $C_{13}$

Chaoliang Tang, Hehui Wu, Shengtong Zhang +1

Let the crown $C_{13}$ be the linear $3$ -graph on $9$ vertices ${a, b, c, d, e, f, g, h, i}$ with edges $E = {{a, b, c}, {a, d, e}, {b, f, g}, {c, h, i}} .$ Proving a conjecture o…

math.CO2021

Graphs with high second eigenvalue multiplicity

Milan Haiman, Carl Schildkraut, Shengtong Zhang +1

Jiang, Tidor, Yao, Zhang, and Zhao recently showed that connected bounded degree graphs have sublinear second eigenvalue multiplicity (always referring to the adjacency matrix). Th…

math.CO2021★ 3 cited

No extremal square-free words over large alphabets

Letong Hong, Shengtong Zhang

A word is square-free if it does not contain any square (a word of the form $X X$ ), and is extremal square-free if it cannot be extended to a new square-free word by inserting a sin…

math.CO2020★ 6 cited

Towards Heim and Neuhauser's Unimodality Conjecture on the Nekrasov-Okounkov polynomials

Letong Hong, Shengtong Zhang

Let $Q_{n} (z)$ be the polynomials associated with the Nekrasov-Okounkov formula $n \geq 1 \sum Q_{n} (z) q^{n} := m = 1 \prod \infty (1 - q^{m})^{- z - 1} .$ In this paper we partially a…

math.CO2020★ 9 cited

Spherical two-distance sets and eigenvalues of signed graphs

Zilin Jiang, Jonathan Tidor, Yuan Yao +2

We study the problem of determining the maximum size of a spherical two-distance set with two fixed angles (one acute and one obtuse) in high dimensions. Let $N_{α, β} (d)$ denote th…

math.CO2019★ 65 cited

Equiangular lines with a fixed angle

Zilin Jiang, Jonathan Tidor, Yuan Yao +2

Solving a longstanding problem on equiangular lines, we determine, for each given fixed angle and in all sufficiently large dimensions, the maximum number of lines pairwise separat…

Hypergraph independence polynomials with a zero close to the origin

A Short Proof to Defant and Kravitz's theorem on the Length of Hitomezashi Loops

Log-Concavity in Powers of Infinite Series Close to (1−z)−1

Domination polynomial is unimodal for large graphs with a universal vertex

Note on the Turán number of the 3-linear hypergraph C13​

Graphs with high second eigenvalue multiplicity

No extremal square-free words over large alphabets

Towards Heim and Neuhauser's Unimodality Conjecture on the Nekrasov-Okounkov polynomials

Spherical two-distance sets and eigenvalues of signed graphs

Equiangular lines with a fixed angle

Log-Concavity in Powers of Infinite Series Close to $(1 - z)^{- 1}$

Note on the Turán number of the $3$ -linear hypergraph $C_{13}$