B. Ho

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math.CO2026

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

Boon Suan Ho, Tomasz Kania

Let $K_{KR}$ denote the optimal Kalton--Roberts constant for approximately additive real-valued set functions on algebras of sets. Kalton and Roberts proved $K_\mathrm{KR}\l…

math.CO2026

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

Boon Suan Ho

ErdÅs 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 di…

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 $I^¸ (n)$ be the number of permutations of ${1, \dots, n}$ with no $3$ -term arithmetic progressions. We prove that $lim_{n \to \infty} I^¸ (n)^{1/ n}$ 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: $h (x^{2}) \geq I ¨ x h (x)$ , where $I ¨ = (1 + 5) /2$ and $h(x)=-x\log x-(1-x)\log(…

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

ErdÅs's diameter conjecture for separated distances fails in high dimensions

The Ferrers bound for spanning trees in bipartite graphs

3AP-free permutations have no exponential growth rate

A generalization of Boppana's entropy inequality

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