Interlace polynomials

M. Aigner, H. Holst, van der

    Research output: Contribution to journalArticleAcademicpeer-review

    41 Citations (Scopus)
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    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.
    Original languageEnglish
    Pages (from-to)11-30
    JournalLinear Algebra and Its Applications
    Volume377
    DOIs
    Publication statusPublished - 2004

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