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Linear independence of derivatives of link polynomials

Authors
Journal
Topology and its Applications
0166-8641
Publisher
Elsevier
Publication Date
Volume
117
Issue
2
Identifiers
DOI: 10.1016/s0166-8641(01)00020-7
Keywords
  • Knots And Links
  • Higher Order Link Polynomials
  • Vassiliev Invariants

Abstract

Abstract Higher order link polynomials were defined by combining ingredients from link polynomials and Vassiliev invariants. It has been proved that each nth partial derivative of the Homfly polynomials is an nth order Homfly polynomial. This naturally raises two questions: Question 1. Are these partial derivatives linearly independent? Question 2. Do they span the space of higher order link polynomials? In this paper, we give an affirmative answer to Question 1. As a by-product, we determine all the higher order Conway polynomials.

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