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Partial chord diagrams and matrix models

Research output: Working paper/Preprint Working paperResearch

  • Jørgen Ellegaard Andersen
  • ,
  • Hiroyuki Fuji, Kagawa University, Japan
  • Masahide Manabe, Warsaw University, Poland
  • Robert C. Penner, Institut Des Hautes Ètudes Scientifiques (IHÉS), CALTECH, California Institute of Technology, Mat Sci, United States
  • Piotr Sulkowski, Warsaw University, California Institute of Technology, Poland
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
Number of pages42
Publication statusPublished - 17 Dec 2016

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