Publication: Research › Working paper

- Jørgen Ellegaard Andersen
- Hiroyuki FujiHiroyuki FujiKagawa UniversityJapan
- Robert C. PennerRobert C. PennerInstitut des Hautes Études Scientifiques (IHÉS)CALTECH, California Institute of Technology, Mat SciUnited States
- Christian ReidysChristian 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 language | English |
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Publisher | arXiv.org |

Number of pages | 16 |

State | Published - 20 Dec 2016 |

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ID: 107471725