Normalizing the Markov trace over the Temperley–Lieb algebra defines one of these functions. One of these functions whose value changes after a type I Reidemeister (“RYE-duh-my-ster”) move is the Kauffman bracket. The initials of six co-discoverers name one of these functions called HOMFLY. Functions of this type commonly used as knot invariants are exemplified by ones named after James Alexander and Vaughan Jones. One sequence of these functions satisfies the relation “T-sub-n evaluated at cosine of theta equals cosine of n times theta,” and is the “first kind” named after Chebyshev. By the Cayley–Hamilton theorem, every square matrix evaluates to zero when plugged into its own characteristic one of these functions. For 10 points, the fundamental theorem of algebra states that what functions have a number of roots equal to their degree? ■END■
ANSWER: polynomials [accept knot polynomials, HOMFLY polynomial, Alexander polynomial, Jones polynomial, Kauffman polynomial; accept Chebyshev polynomial or Chebyshev polynomial of the first kind; accept characteristic polynomial; prompt on knot invariants until read]
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= Average correct buzz position