11 citations · 47 across the 48 of their papers we have counts for
Showing 2018 · math.COShow all
3 papers · 2 filters
math.CO2018
Difference between families of weakly and strongly maximal integral lattice-free polytopes
Gennadiy Averkov
A -dimensional closed convex set in is said to be lattice-free if the interior of is disjoint with . We consider the following two families…
math.CO2018
Local optimality of Zaks-Perles-Wills simplices
Gennadiy Averkov
In 1982, Zaks, Perles and Wills discovered a d-dimensional lattice simplex S_{d,k} with k interior lattice points, whose volume is linear in k and doubly exponential in the dimensi…
math.CO2018
Equality case in van der Corput's inequality and collisions in multiple lattice tilings
Gennadiy Averkov
Van der Corput's provides the sharp bound vol(C) \le m 2^d on the volume of a d-dimensional origin-symmetric convex body C that has 2m-1 points of the integer lattice in its interi…