Abstract
For a knot, the ascending number is the minimum number of crossing changes which are needed to obtain an descending diagram. We study relations between the ascending number and geometrical invariants; the crossing number, the genus and the bridge index. The main aim of this paper is to show that there exists a knot K such that [Formula: see text] and [Formula: see text], and that there exists a knot K’ such that [Formula: see text] and [Formula: see text] for any positive integer n. We also give an upper bound of the ascending number for a 2-bridge knot.
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