اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدNo lattice tiling of $mathbb{Z}^n$ by Lee Sphere of radius 2
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We prove the nonexistence of lattice tilings of $mathbb{Z}^n$ by Lee spheres of radius $2$ for all dimensions $ngeq 3$. This implies that the Golomb-Welch conjecture is true when the common radius of the Lee spheres equals $2$ and $2n^2+2n+1$ is a prime. As a direct consequence, we also answer an open question in the degree-diameter problem of graph theory: the order of any abelian Cayley graph of diameter $2$ and degree larger than $5$ cannot meet the abelian Cayley Moore bound.
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