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

Research output: Working paper › Research

- Jørgen Ellegaard Andersen
Hiroyuki Fuji, Kagawa University, JapanRobert C. Penner, Institut des Hautes Études Scientifiques (IHÉS), CALTECH, California Institute of Technology, Mat Sci, United StatesChristian Reidys, Biocomplexity Institute of Virginia Tech, United 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 |
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Number of pages | 16 |
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State | Published - 20 Dec 2016 |
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ID: 107471725