标题： 关于六个、七个和八个球体的排列：单原子离子化合物的最大键合 显示英文标题

标题： On Arrangements of Six, Seven, and Eight Spheres: Maximal Bonding of Monatomic Ionic Compounds

摘要： 设$C(n)$为接触数问题的解，即在$\mathbb{R}^3$中任何由$n$个全等球体组成的排列中，接触对的最大数目。 我们证明了长期猜想的$C(6)=12, C(7)=15$和$C(8)=18$的值。 该证明策略在广泛的案例分析下推广到$C(9)=21, C(10) = 25, C(11) = 29, C(12) = 33$和$C(13) = 36$。 这些结果在凝聚态物理、材料科学、晶体学、界面有机化学和物理化学中具有重要意义。 显示英文摘要

摘要： Let $C(n)$ be the solution to the contact number problem, i.e., the maximum number of touching pairs among any packing of $n$ congruent spheres in $\mathbb{R}^3$. We prove the long conjectured values of $C(6)=12, C(7)=15$, and $C(8)=18$. The proof strategy generalizes under an extensive case analysis to $C(9)=21, C(10) = 25, C(11) = 29, C(12) = 33$, and $C(13) = 36$. These results have great importance for condensed matter physics, materials science, crystallography, organic and physical chemistry of interfaces.