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The lexicographic degree of the first two-bridge knots
Erwan Brugallé, Pierre-Vincent Koseleff, Daniel Pecker
We study the degree of polynomial representations of knots. We give the lexicographic degree of all two-bridge knots with 11 or fewer crossings. First, we estimate the total degree…
Untangling trigonal diagrams
Erwan Brugallé, Pierre-Vincent Koseleff, Daniel Pecker
Let be a link of Conway's normal form , , or with $mn\textgreater{}0$, and let be a trigonal diagram of We show that it is possible to transfo…
On the lexicographic degree of two-bridge knots
Erwan Brugallé, Pierre-Vincent Koseleff, Daniel Pecker
We study the degree of polynomial representations of knots. We obtain the lexicographic degree for two-bridge torus knots and generalized twist knots. The proof uses the braid theo…