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math.MG2018
On the Voronoi Conjecture for combinatorially Voronoi parallelohedra in dimension five
Mathieu Dutour Sikirić, Alexey Garber, Alexander Magazinov
In a recent paper Garber, Gavrilyuk and Magazinov proposed a sufficient combinatorial condition for a parallelohedron to be affinely Voronoi. We show that this condition holds for…
math.MG2018
On the Origin of Crystallinity: a Lower Bound for the Regularity Radius of Delone Sets
Igor A. Baburin, Mikhail Bouniaev, Nikolay Dolbilin +4
The local theory of regular or multi-regular systems aims at finding sufficient local conditions for a Delone set to be a regular or multi-regular system. One of the main goals…