For an oriented knot diagram, we define a cyclic word in letters P and N corresponding to positive and negative crossings along the diagram, respectively. We give a necessary and sufficient condition for a cyclic word in P and N to be obtained from some knot diagram. Also, we prove that any PN sequence of a diagram of a nontrivial knot contains at least four subsequences PP and NN.
|ジャーナル||Journal of Knot Theory and its Ramifications|
|出版ステータス||Published - 2016 9月 1|
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