<s>
Skein	B-Application
relations	I-Application
are	O
a	O
mathematical	O
tool	O
used	O
to	O
study	O
knots	O
.	O
</s>
<s>
Skein	B-Application
relations	I-Application
are	O
often	O
used	O
to	O
give	O
a	O
simple	O
definition	O
of	O
knot	O
polynomials	O
.	O
</s>
<s>
A	O
skein	B-Application
relation	I-Application
gives	O
a	O
linear	O
relation	O
between	O
the	O
values	O
of	O
a	O
knot	O
polynomial	O
on	O
a	O
collection	O
of	O
three	O
links	O
which	O
differ	O
from	O
each	O
other	O
only	O
in	O
a	O
small	O
region	O
.	O
</s>
<s>
For	O
some	O
knot	O
polynomials	O
,	O
such	O
as	O
the	O
Conway	O
,	O
Alexander	O
,	O
and	O
Jones	O
polynomials	O
,	O
the	O
relevant	O
skein	B-Application
relations	I-Application
are	O
sufficient	O
to	O
calculate	O
the	O
polynomial	O
recursively	O
.	O
</s>
<s>
A	O
skein	B-Application
relationship	I-Application
requires	O
three	O
link	O
diagrams	O
that	O
are	O
identical	O
except	O
at	O
one	O
crossing	O
.	O
</s>
<s>
Depending	O
on	O
the	O
knot	O
polynomial	O
in	O
question	O
,	O
the	O
links	O
(	O
or	O
tangles	O
)	O
appearing	O
in	O
a	O
skein	B-Application
relation	I-Application
may	O
be	O
oriented	O
or	O
unoriented	O
.	O
</s>
<s>
More	O
formally	O
,	O
a	O
skein	B-Application
relation	I-Application
can	O
be	O
thought	O
of	O
as	O
defining	O
the	O
kernel	O
of	O
a	O
quotient	O
map	O
from	O
the	O
planar	B-Application
algebra	I-Application
of	O
tangles	O
.	O
</s>
<s>
Sometime	O
in	O
the	O
early	O
1960s	O
,	O
Conway	O
showed	O
how	O
to	O
compute	O
the	O
Alexander	O
polynomial	O
using	O
skein	B-Application
relations	I-Application
.	O
</s>
<s>
As	O
it	O
is	O
recursive	O
,	O
it	O
is	O
not	O
quite	O
so	O
direct	O
as	O
Alexander	O
's	O
original	O
matrix	B-Architecture
method	O
;	O
on	O
the	O
other	O
hand	O
,	O
parts	O
of	O
the	O
work	O
done	O
for	O
one	O
knot	O
will	O
apply	O
to	O
others	O
.	O
</s>
