  Through a series of papers in the 1980's, Bouchet introduced isotropic
systems and the Tutte-Martin polynomial of an isotropic system. Then, Arratia,
Bollob\'as, and Sorkin developed the interlace polynomial of a graph in [ABS00]
in response to a DNA sequencing application. The interlace polynomial has
generated considerable recent attention, with new results including realizing
the original interlace polynomial by a closed form generating function
expression instead of by the original recursive definition (see Aigner and van
der Holst [AvdH04], and Arratia, Bollob\'as, and Sorkin [ABS04b]). Now, Bouchet
[Bou05] recognizes the vertex-nullity interlace polynomial of a graph as the
Tutte-Martin polynomial of an associated isotropic system. This suggests that
the machinery of isotropic systems may be well-suited to investigating
properties of the interlace polynomial. Thus, we present here an alternative
proof for the closed form presentation of the vertex-nullity interlace
polynomial using the machinery of isotropic systems. This approach both
illustrates the intimate connection between the vertex-nullity interlace
polynomial and the Tutte-Martin polynomial of an isotropic system and also
provides a concrete example of manipulating isotropic systems. We also provide
a brief survey of related work.
