For two subsets
and
of
with
and
, we define their
coincidence by
. A
family
is called
-coinciding if
for all distinct
. It is conjectured
that for
a
-coinciding family has size
at most
. The conjecture
is confirmed for cases
,
the case
, and
the case
,
. The opposite problem,
where
-subsets are
forbidden to coincide in
or more elements leads to new types of designs. We solve the new design problem completely
for the
case.
Keywords
extremal set theory, ordered intersection, $t$-coinciding