The successive minima
of an origin-symmetric convex body
with respect to a full-rank point
lattice
measure the scales needed to obtain independent lattice
points. The
th
successive minimum is the least
such that
contains
linearly independent
points of
.
The convex body is assumed compact,
with the origin in its interior
(Betke et al. 1993, Aliev and Henk 2023).
For a nonsymmetric convex body , lattice-point inequalities often use the successive minima
of its symmetrized difference body
. Here
denotes a Minkowski
sum with
,
rather than set-theoretic subtraction.