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Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.
Abstract Heilbronn's triangle problem is a classical question in discrete geometry. It asks to determine the smallest number Δ=Δ(N)$\Delta = \Delta (N)$ for which every collection in N$N$ points in the unit square spans a triangle with area at most Δ$\Delta$.
Dmitrii Zakharov
wiley +1 more source

Diophantine tuples and product sets in shifted powers

Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.
Abstract Let k⩾2$k\geqslant 2$ and n≠0$n\ne 0$. A Diophantine tuple with property Dk(n)$D_k(n)$ is a set of positive integers A$A$ such that ab+n$ab+n$ is a k$k$th power for all a,b∈A$a,b\in A$ with a≠b$a\ne b$. Such generalizations of classical Diophantine tuples have been studied extensively.
Ernie Croot, Chi Hoi Yip
wiley +1 more source

Coding and anticoding of a cardinal by bounded subsets of the cardinal

Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.
Abstract This paper will consider combinatorial properties related to coding a cardinal by its bounded subsets. These properties have traditionally been studied in the context of very large cardinals and variations of these properties either reach the level of Kunen inconsistency or are very close to it.
William Chan
wiley +1 more source

Advances of Quantum Key Distribution and Network Nonlocality. [PDF]

Entropy (Basel)
Geng M.
europepmc +1 more source

A generalization of Ramsey theory for graphs