B. Ho

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20192026

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Showing 2026 · math.COShow all

7 papers · 2 filters

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.CO2026

Counterexamples to a dimension-free variant of Erdős's diameter conjecture for separated distances

Boon Suan Ho

Erdős asked about the least possible diameter of an $n$ -point set in Euclidean space when any two pairwise distances differ by at least $1$ . We consider the uniform-in-dimension va…

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-…