ON AN ESTIMATION OF FLAT PLUMBING BASKET NUMBER OF KNOTS
For a knot K, Hirose and Nakashima introduced a numerical invariant called flat plumbing basket number, denoted which is the minimal number of annuli to obtain a flat plumbing basket of K. They gave two estimations of using the degree of the Alexander polynomial of K. In this paper, we introduce a basket diagram to represent a basket, which is an extension of a flat plumbing basket diagram, and introduce some operations on basket diagrams. Then we show that one of the estimations given by Hirose and Nakashima is exact by using these operations.
knots and links, Seifert surface, flat plumbing basket.