<s>
In	O
the	O
study	O
of	O
permutations	B-Algorithm
and	O
permutation	B-Algorithm
patterns	I-Algorithm
,	O
a	O
permutation	B-Algorithm
class	I-Algorithm
is	O
a	O
set	O
of	O
permutations	B-Algorithm
such	O
that	O
every	O
pattern	O
within	O
a	O
permutation	B-Algorithm
in	O
is	O
also	O
in	O
.	O
</s>
<s>
In	O
other	O
words	O
,	O
a	O
permutation	B-Algorithm
class	I-Algorithm
is	O
a	O
hereditary	O
property	O
of	O
permutations	B-Algorithm
,	O
or	O
a	O
downset	O
in	O
the	O
permutation	B-Algorithm
pattern	I-Algorithm
order	O
.	O
</s>
<s>
A	O
permutation	B-Algorithm
class	I-Algorithm
may	O
also	O
be	O
known	O
as	O
a	O
pattern	O
class	O
,	O
closed	O
class	O
,	O
or	O
simply	O
class	O
of	O
permutations	B-Algorithm
.	O
</s>
<s>
Every	O
permutation	B-Algorithm
class	I-Algorithm
can	O
be	O
defined	O
by	O
the	O
minimal	O
permutations	B-Algorithm
which	O
do	O
not	O
lie	O
inside	O
it	O
,	O
its	O
basis	O
.	O
</s>
<s>
A	O
principal	O
permutation	B-Algorithm
class	I-Algorithm
is	O
a	O
class	O
whose	O
basis	O
consists	O
of	O
only	O
a	O
single	O
permutation	B-Algorithm
.	O
</s>
<s>
Thus	O
,	O
for	O
instance	O
,	O
the	O
stack-sortable	B-Algorithm
permutations	I-Algorithm
form	O
a	O
principal	O
permutation	B-Algorithm
class	I-Algorithm
,	O
defined	O
by	O
the	O
forbidden	O
pattern	O
231	O
.	O
</s>
<s>
However	O
,	O
some	O
other	O
permutation	B-Algorithm
classes	O
have	O
bases	O
with	O
more	O
than	O
one	O
pattern	O
or	O
even	O
with	O
infinitely	O
many	O
patterns	O
.	O
</s>
<s>
A	O
permutation	B-Algorithm
class	I-Algorithm
that	O
does	O
not	O
include	O
all	O
permutations	B-Algorithm
is	O
called	O
proper	O
.	O
</s>
<s>
In	O
the	O
late	O
1980s	O
,	O
Richard	O
Stanley	O
and	O
Herbert	O
Wilf	O
conjectured	O
that	O
for	O
every	O
proper	O
permutation	B-Algorithm
class	I-Algorithm
,	O
there	O
is	O
some	O
constant	O
such	O
that	O
the	O
number	O
of	O
length	O
-	O
permutations	B-Algorithm
in	O
the	O
class	O
is	O
upper	O
bounded	O
by	O
.	O
</s>
<s>
exists	O
for	O
all	O
principal	O
permutation	B-Algorithm
classes	O
,	O
it	O
is	O
open	O
whether	O
it	O
exists	O
for	O
all	O
other	O
permutation	B-Algorithm
classes	O
.	O
</s>
<s>
Two	O
permutation	B-Algorithm
classes	O
are	O
called	O
Wilf	O
equivalent	O
if	O
,	O
for	O
every	O
,	O
both	O
have	O
the	O
same	O
number	O
of	O
permutations	B-Algorithm
of	O
length	O
.	O
</s>
<s>
They	O
are	O
the	O
combinatorial	O
classes	O
of	O
permutation	B-Algorithm
classes	O
.	O
</s>
<s>
The	O
counting	O
functions	O
and	O
Wilf	O
equivalences	O
among	O
many	O
specific	B-Algorithm
permutation	I-Algorithm
classes	I-Algorithm
are	O
known	O
.	O
</s>
