A 1-variable unoriented knot polynomial 
. It satisfies
 |
(1)
|
and the skein relationship
 |
(2)
|
It also satisfies
 |
(3)
|
where 
is the knot sum and
 |
(4)
|
where 
is the mirror image of 
. The BLM/Ho polynomials of mutant
knots are also identical. Brandt et al. (1986) give a number of interesting
properties. For any link 
with 
components, 
is divisible by 
. If 
has 
components, then the lowest power
of 
in 
is 
,
and
 |
(5)
|
where 
is the HOMFLY polynomial. Also, the degree of
is less than the link
crossing number of 
. If 
is a 2-bridge knot, then
 |
(6)
|
where 
(Kanenobu and Sumi 1993).
The polynomial was subsequently extended to the 2-variable Kauffman polynomial F, which satisfies
 |
(7)
|
Brandt et al. (1986) give a listing of 
polynomials for knots
up to 8 crossings and links up to 6 crossings.
