The boundary length and point spectrum enumeration of partial chord diagrams using cut and join recursion

Publication: ResearchWorking paper

  • Jørgen Ellegaard Andersen
  • Hiroyuki Fuji
    Hiroyuki FujiKagawa UniversityJapan
  • Robert C. Penner
    Robert C. PennerInstitut des Hautes Études Scientifiques (IHÉS)CALTECH, California Institute of Technology, Mat SciUnited States
  • Christian Reidys
    Christian ReidysBiocomplexity Institute of Virginia TechUnited States
We introduce the boundary length and point spectrum, as a joint generalization of the boundary length spectrum and boundary point spectrum in [1]. We establish by cut-and-join methods that the number of partial chord diagrams filtered by the boundary length and point spectrum satisfies a recursion relation, which combined with an initial condition determines these numbers uniquely. This recursion relation is equivalent to a second order, non-linear, algebraic partial differential equation for the generating function of the numbers of partial chord diagrams filtered by the boundary length and point spectrum.
Original languageEnglish
PublisherarXiv.org
Number of pages16
StatePublished - 20 Dec 2016

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