B. Ho

activity

20192026

collaborators

11 papers

math.CO2026

Greedy queens and the golden ratio

Boon Suan Ho

Place a queen in each successive column of an infinite $N \times N$ chessboard, always choosing the lowest row such that no two queens may attack one another. We pr…

math.CO2026

A 4AP-free permutation of the positive integers

Boon Suan Ho

We construct a permutation of the positive integers containing no four-term arithmetic progression as a subsequence.

math.CO2026

Halving the original Kalton--Roberts upper bound for nearly additive set functions

Boon Suan Ho, Tomasz Kania

Let $K_{K R}$ be the least constant governing uniform approximation of approximately additive real-valued set functions by finitely additive signed measures. We prove that $$K_{KR}\…

math.CA2026

Counterexamples for lacunary dilates via dyadic spike blocks

Boon Suan Ho

We construct dyadic lacunary counterexamples for two problems of Erdős on pointwise behavior of dilates on the circle. The main device is a dyadic spike block: rare positive spikes…

math.CO2026

Erdős's diameter conjecture for separated distances fails in high dimensions

Boon Suan Ho

Erdős asked whether every $n$ -point set in Euclidean space whose $(2 n)$ pairwise distances are mutually at least $1$ apart must have diameter at least $(1 + o (1)) n^{2}$ . We dis…

math.MG2026

A new lower bound for the kissing number in 19 dimensions

Boon Suan Ho

We prove that the kissing number in 19 dimensions is at least 11948, improving the bound of Cohn and Li by 256. By the odd-sign construction of Cohn and Li, it is enough to find a…

math.CO2026

The Ferrers bound for spanning trees in bipartite graphs

Boon Suan Ho

We prove Ehrenborg's conjecture that every connected bipartite graph $G$ with parts of size $m$ and $n$ has at most $\frac{1}{mn} \prod_{v \in V (G)} deg (v)$ spanning t…

math.CO2026

3AP-free permutations have no exponential growth rate

Boon Suan Ho

Let $θ (n)$ be the number of permutations of ${1, \dots, n}$ with no $3$ -term arithmetic progressions. We prove that $lim_{n \to \infty} θ (n)^{1/ n}$ does not exist.

math.CO2026

A generalization of Boppana's entropy inequality

Boon Suan Ho

In recent progress on the union-closed sets conjecture, a key lemma has been Boppana's entropy inequality: $h (x^{2}) \geq ϕ x h (x)$ , where $ϕ = (1 + 5) /2$ and $h(x)=-x\log x-(1-x)\log(1-…

math.CO2023

Two product formulas for counting successive vertex orderings

Boon Suan Ho

A vertex ordering of a graph $G$ is a bijection $π : {1, \dots, ∣ V (G) ∣} \to V (G)$ . It is successive if the induced subgraph $G [v_{π (1)}, \dots, v_{π (k)}]$ is connected for each $k$ …

math.CO2019

Equality cases for a bound on the chromatic number

Boon Suan Ho, Joel Junyao Tan, Xiaorui Zhang

It is known that the inequality $\frac{χ ( G ) ( χ ( G ) - 1 )}{2} + ∣ V ∣ - χ (G) \leq ∣ E ∣$ holds for all connected graphs, where $χ (G)$ denotes the chromatic number of $G$ . We prove that eq…