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A Note on Some Link Polynomials
Author(s) -
Lipson A. S.
Publication year - 1988
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/20.5.532
Subject(s) - mathematics , invariant (physics) , link (geometry) , discrete mathematics , set (abstract data type) , pure mathematics , combinatorics , algebra over a field , computer science , mathematical physics , programming language
Hass and Wajnryb [2] have given a set of sufficient conditions for a recursive definition over crossing changes in link diagrams to provide a well‐defined link invariant in a similar way to [3]. They also provide a number of examples satisfying these conditions, including a number with non‐linear recursive definitions. I here show that all of these examples are in fact special cases of the known invariant P ( l, m ) of [3, 1]. In particular, there exists no linear recursive definition providing an invariant not covered by P ( l, m ).