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A note on distinct differences in
t
t
t
-intersecting families
Authors
Jagannath Bhanja
Sayan Goswami
Publication date
8 November 2022
Publisher
View
on
arXiv
Abstract
For a family
F
\mathcal{F}
F
of subsets of
{
1
,
2
,
β¦
,
n
}
\{1,2,\ldots,n\}
{
1
,
2
,
β¦
,
n
}
, let
D
(
F
)
=
{
F
β
G
:
F
,
G
β
F
}
\mathcal{D}(\mathcal{F}) = \{F\setminus G: F, G \in \mathcal{F}\}
D
(
F
)
=
{
F
β
G
:
F
,
G
β
F
}
be the collection of all (setwise) differences of
F
\mathcal{F}
F
. The family
F
\mathcal{F}
F
is called a
t
t
t
-intersecting family, if for some positive integer
t
t
t
and any two members
F
,
G
β
F
F, G \in \mathcal{F}
F
,
G
β
F
we have
β£
F
β©
G
β£
β₯
t
|F\cap G| \geq t
β£
F
β©
G
β£
β₯
t
. The family
F
\mathcal{F}
F
is simply called intersecting if
t
=
1
t=1
t
=
1
. Recently, Frankl proved an upper bound on the size of
D
(
F
)
\mathcal{D}(\mathcal{F})
D
(
F
)
for the intersecting families
F
\mathcal{F}
F
. In this note we extend the result of Frankl to
t
t
t
-intersecting families
Similar works
Full text
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oai:arXiv.org:2211.04081
Last time updated on 12/12/2022