An estimation for the ascending numbers of knots by Γ-polynomials

Abstract

For a knot, the ascending number is the minimum number of crossing changes which are needed to obtain an descending diagram. We study the [Formula: see text]-polynomial of knots with a given ascending number. We give a lower bound of the ascending numbers by using [Formula: see text]-polynomials. We estimate the ascending numbers for 65 prime knots up to 10 crossings by using [Formula: see text]-polynomials, Conway polynomials, and the determinants.