A
-subset partition,
or
-subpartition,
is a
-subset of an
-set that is partitioned
into
distinct blocks,
each of size
. Two
-subpartitions are
said to
-intersect if
they have at least
blocks in common. In this paper, we prove an Erdős–Ko–Rado theorem for intersecting families
of
-subpartitions.
We show that for
,
and
, the number of
-subpartitions in the
largest
-intersecting
family is at most
,
and that this bound is only attained by the family of
-subpartitions
with a common fixed block, known as the
canonical intersecting family of-subpartitions. Further,
provided that
is
sufficiently large relative to
and
, the largest
-intersecting family is the
family of
-subpartitions that
contain a common set of
fixed blocks.