A decomposition theorem for the linking polynomial of two matroids

In [W. Kook, V. Reiner, D. Stanton, A convolution formula for the Tutte polynomial, J. Combin. Theory Ser. B 76 (1999) 297–300], it is proved that the Tutte polynomial of a matroid can be decomposed into a colouring factor and a flow factor as follows:T(M;x,y)=∑X⊆ET(M|X;0,y)T(M/X;x,0).We extend this decomposition to the linking polynomial of two matroids defined in [D.J.A. Welsh, K.K. Kayibi, A linking polynomial of two matroids, Adv. in Appl. Math. 32 (2004) 391–419].