A Note on Some Link Polynomials

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 ).