2-Adjacency between some special knots and pretzel knot

摘要

We study 2-adjacency between a classical (3-strand) pretzel knot and the trefoil knot or the figure-eight knot by using the early results about classical pretzel knots and their polynomials and elementary number theory. We show that except for the trefoil knot or the figure-eight knot, a nontrivial classical pretzel knot is not 2-adjacent to either of them, and vice versa.