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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, Japan
- Robert C. Penner, Institut des Hautes Études Scientifiques (IHÉS), CALTECH, California Institute of Technology, Mat Sci, United States
- Christian 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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Publication status | Published - 20 Dec 2016 |
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ID: 107471725