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On the existence of dense substructures in finite groups
Ching Wong
Fix . We prove that any large enough finite group contains elements which span quadratically many triples of the form , given any dense s…
The Brown-Erdős-Sós Conjecture in finite abelian groups
Jozsef Solymosi, Ching Wong
The Brown-Erdős-Sós conjecture, one of the central conjectures in extremal combinatorics, states that for any integer if a 3-uniform hypergraph on vertices contains…
An application of kissing numbers in sum-product estimates
Jozsef Solymosi, Ching Wong
The boundedness of the kissing numbers of convex bodies has been known to Hadwiger for long. We present an application of it to the sum-product estimate $$\max(|\mathcal{A}+\mathca…
Cycles in graphs of fixed girth with large size
József Solymosi, Ching Wong
Consider a family of graphs having a fixed girth and a large size. We give an optimal lower asymptotic bound on the number of even cycles of any constant length, as the order of th…