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arXiv · 1612.06482

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

Jørgen Ellegaard Andersen·Hiroyuki Fuji·Robert C. Penner·Christian M. Reidys
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Abstract

We introduce the boundary length and point spectrum, as a joint generalization of the boundary length spectrum and boundary point spectrum in arXiv:1307.0967. 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.

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Jørgen Ellegaard Andersen, Hiroyuki Fuji, Robert C. Penner, Christian M. Reidys. 2016-12-20. The boundary length and point spectrum enumeration of partial chord diagrams using cut and join recursion. https://arxiv.org/abs/1612.06482

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