<s>
The	O
concept	O
of	O
alternating	B-Application
planar	I-Application
algebras	I-Application
first	O
appeared	O
in	O
the	O
work	O
of	O
Hernando	O
Burgos-Soto	O
on	O
the	O
Jones	O
polynomial	O
of	O
alternating	O
tangles	O
.	O
</s>
<s>
Alternating	B-Application
planar	I-Application
algebras	I-Application
provide	O
an	O
appropriate	O
algebraic	O
framework	O
for	O
other	O
knot	O
invariants	O
in	O
cases	O
the	O
elements	O
involved	O
in	O
the	O
computation	O
are	O
alternating	O
.	O
</s>
<s>
An	O
alternating	B-Application
planar	I-Application
algebra	I-Application
is	O
an	O
oriented	O
planar	B-Application
algebra	I-Application
,	O
where	O
the	O
-input	O
planar	O
arc	O
diagrams	O
satisfy	O
the	O
following	O
conditions	O
:	O
</s>
<s>
There	O
are	O
two	O
known	O
applications	O
of	O
the	O
concept	O
of	O
alternating	B-Application
planar	I-Application
algebra	I-Application
.	O
</s>
