9 papers · 1 filter
Greedy queens and the golden ratio
Boon Suan Ho
Place a queen in each successive column of an infinite chessboard, always choosing the lowest row such that no two queens may attack one another. We pr…
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.
Halving the original Kalton--Roberts upper bound for nearly additive set functions
Boon Suan Ho, Tomasz Kania
Let be the least constant governing uniform approximation of approximately additive real-valued set functions by finitely additive signed measures. We prove that $$K_{KR}\…
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…
Erdős's diameter conjecture for separated distances fails in high dimensions
Boon Suan Ho
Erdős asked whether every -point set in Euclidean space whose pairwise distances are mutually at least apart must have diameter at least . We dis…
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…
The Ferrers bound for spanning trees in bipartite graphs
Boon Suan Ho
We prove Ehrenborg's conjecture that every connected bipartite graph with parts of size and has at most spanning t…
3AP-free permutations have no exponential growth rate
Boon Suan Ho
Let be the number of permutations of with no -term arithmetic progressions. We prove that does not exist.
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: , where and $h(x)=-x\log x-(1-x)\log(1-…