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

PRABHAKAR MADETI

Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati - 781 039, India

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and

RAMA MISHRA

Indian Institute of Science Education and Research, Pune - 411 021, India

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https://doi.org/10.1142/S021821650900704XCited by:2 (Source: Crossref)

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.

Keywords:

AMSC: 57M25, 14P25

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