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Symmetric groups and expanders
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We construct explicit generating sets
F
n
F_n
and
F
~
n
\tilde F_n
of the alternating and the symmetric groups, which turn the Cayley graphs
C
(
A
l
t
(
n
)
,
F
n
)
\mathcal {C}(\mathrm {Alt}(n), F_n)
and
C
(
S
y
m
(
n
)
,
F
~
n
)
\mathcal {C}(\mathrm {Sym}(n), \tilde F_n)
into a family of bounded degree expanders for all sufficiently large
n
n
. These expanders have many applications in the theory of random walks on groups and in other areas of mathematics.
American Mathematical Society (AMS)
Title: Symmetric groups and expanders
Description:
We construct explicit generating sets
F
n
F_n
and
F
~
n
\tilde F_n
of the alternating and the symmetric groups, which turn the Cayley graphs
C
(
A
l
t
(
n
)
,
F
n
)
\mathcal {C}(\mathrm {Alt}(n), F_n)
and
C
(
S
y
m
(
n
)
,
F
~
n
)
\mathcal {C}(\mathrm {Sym}(n), \tilde F_n)
into a family of bounded degree expanders for all sufficiently large
n
n
.
These expanders have many applications in the theory of random walks on groups and in other areas of mathematics.
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