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Abstract
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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.
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Keywords
extremal set theory, ordered intersection, $t$-coinciding
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Mathematical Subject Classification
Primary: 05D05
Secondary: 05B30
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Milestones
Received: 11 October 2023
Revised: 18 March 2024
Accepted: 3 April 2024
Published: 16 May 2024
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Publishers). |
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