Partial chord diagrams and matrix models

Publication: ResearchWorking paper

  • Jørgen Ellegaard Andersen
  • Hiroyuki Fuji
    Hiroyuki FujiKagawa UniversityJapan
  • Masahide Manabe
    Masahide ManabeWarsaw UniversityPoland
  • Robert C. Penner
    Robert C. PennerInstitut des Hautes Études Scientifiques (IHÉS)CALTECH, California Institute of Technology, Mat SciUnited States
  • Piotr Sulkowski
    Piotr SulkowskiWarsaw UniversityCalifornia Institute of TechnologyPoland
In this article, the enumeration of partial chord diagrams is discussed via matrix model techniques. In addition to the basic data such as the number of backbones and chords, we also consider the Euler characteristic, the backbone spectrum, the boundary point spectrum, and the boundary length spectrum. Furthermore, we consider the boundary length and point spectrum that unifies the last two types of spectra. We introduce matrix models that encode generating functions of partial chord diagrams filtered by each of these spectra. Using these matrix models, we derive partial differential equations – obtained independently by cut-and-join arguments in an earlier work – for the corresponding generating functions.
Original languageEnglish
PublisherarXiv.org
Number of pages42
StatePublished - 17 Dec 2016

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