Corrigendum to "A linking polynomial of two matroids" [Adv. in Appl. Math. 32 (1-2) (2004) 391-419]
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We wish to point out that the 4-variable linking polynomial Q (M, N) of two matroids M , N defined in [4] is equivalent to the three-variable Tutte polynomial t(M, N) of a matroid perspective introduced by Michel Las Vergnas in [1]. To show this, one needs to extend the definition of the matroid perspective Tutte polynomial t(M, N) via its rank generating function so that then it is well defined for all matroid pairs M, N . With this extended definition, it is easy to see that Q (M, N) and t(M, N) differ only by a simple multiplicative factor. We give details of this transformation on p. 394 of [4] for the case when (M, N) is a matroid perspective. Using this correspondence, it is straightforward to see that Theorem 3 and its corollaries from [4, Section 6] are direct consequences of Theorem 8.1 of [3] (first announced as Theorem 6.1 in the extended abstract [2]). Rather than being a new result, Theorem 3 of [4] is, in fact, a theorem of Las Vergnas, and should be quoted as such. We are very grateful to Michel Las Vergnas for pointing this out and apologize to him for initially overlooking his work.
[1] Dominic Welsh,et al. A linking polynomial of two matroids , 2004, Adv. Appl. Math..
[2] Michel Las Vergnas,et al. The Tutte polynomial of a morphism of matroids I. Set-pointed matroids and matroid perspectives , 1999 .
[3] Michel Las Vergnas,et al. On the Tutte Polynomial of a Morphism of Matroids , 1980 .