The bracket polynomial
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The bracket polynomial book
This chapter introduces the normalized Kauffman bracket polynomial, which is sometimes referred to as the bracket polynomial or the f-polynomial. It focuses on theorems that relate the bracket polynomial and properties of the links. In these theorems, quantifiers play an important role. The normalized Kauffman bracket polynomial is an invariant of oriented links that was defined by Louis Kauffman in 1987. The f-polynomial is a combinatorial reformulation of the Jones polynomial that is known for its recursive computational formula. The skein relation is applied recursively to a virtual link diagram. Each application produces two new link diagrams, each with one less classical crossing. Virtualization involves taking a single classical crossing and flanking the crossing with two virtual crossings. There are two possible methods of virtualization, depending on whether one wants to preserve the over passing strand or the sign of the crossing.