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Cameron-Liebler sets in permutation groups
Authors
Jozefien D'haeseleer
Karen Meagher
Venkata Raghu Tej Pantangi
Publication date
16 August 2023
Publisher
View
on
arXiv
Abstract
Consider a group
G
G
G
acting on a set
Ω
\Omega
Ω
, the vector
v
a
,
b
v_{a,b}
v
a
,
b
​
is a vector with the entries indexed by the elements of
G
G
G
, and the
g
g
g
-entry is 1 if
g
g
g
maps
a
a
a
to
b
b
b
, and zero otherwise. A
(
G
,
Ω
)
(G,\Omega)
(
G
,
Ω
)
-Cameron-Liebler set is a subset of
G
G
G
, whose indicator function is a linear combination of elements in
{
v
a
,
b
Â
:
Â
a
,
b
∈
Ω
}
\{v_{a, b}\ :\ a, b \in \Omega\}
{
v
a
,
b
​
Â
:
Â
a
,
b
∈
Ω
}
. We investigate Cameron-Liebler sets in permutation groups, with a focus on constructions of Cameron-Liebler sets for 2-transitive groups.Comment: 25 page
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Last time updated on 18/08/2023