MINIMAL DEGREE SEQUENCE FOR TORUS KNOTS OF TYPE (p, q)

Abstract

In this paper we prove the following result: for coprime positive integers p and q with p < q, if r is the least positive integer such that 2p-1 and q + r are coprime, then the minimal degree sequence for a torus knot of type (p, q) is the triple (2p - 1, q + r, d) or (q + r, 2p - 1, d) where q + r + 1 ≤ d ≤ 2q - 1.