The bracket polynomial is one-variable knot polynomial related to the Jones polynomial. The bracket
polynomial, however, is not a topological invariant, since it is changed by
type I Reidemeister moves. However, the polynomial span of the bracket polynomial is a knot
invariant, as is a normalized form involving the writhe.
The bracket polynomial is occasionally given the grandiose name regular isotopy invariant.
It is defined by

(1)

where
and
are the "splitting variables," runs through all "states" of obtained by splitting the link, is the product of "splitting labels"
corresponding to ,
and

Adams, C. C. The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots.
New York: W. H. Freeman, pp. 148-155 and 157-158, 1994.Kauffman,
L. "New Invariants in the Theory of Knots." Amer. Math. Monthly95,
195-242, 1988.Kauffman, L. Knots
and Physics. Teaneck, NJ: World Scientific, pp. 25-29, 1991.Livingston,
C. "Kauffman's Bracket Polynomial." Knot
Theory. Washington, DC: Math. Assoc. Amer., pp. 217-220, 1993.