Abstract
In a recent paper Arratia, Bollobás and Sorkin discuss a graph polynomial defined recursively, which they call the interlace polynomial q( G, x). They present several interesting results with applications to the Alexander polynomial and state the conjecture that | q( G,−1)| is always a power of 2. In this paper we use a matrix approach to study q( G, x). We derive evaluations of q( G, x) for various x, which are difficult to obtain (if at all) by the defining recursion. Among other results we prove the conjecture for x=−1. A related interlace polynomial Q( G, x) is introduced. Finally, we show how these polynomials arise as the Martin polynomials of a certain isotropic system as introduced by Bouchet.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
