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

Autor:	Andersen, Jørgen Ellegaard, Fuji, Hiroyuki, Penner, Robert C., Reidys, Christian M.
Rok vydání:	2016
Předmět:	Mathematical Physics High Energy Physics - Theory Mathematics - Combinatorics Quantitative Biology - Quantitative Methods
Zdroj:	Trav. Math. 25 (2017) 213
Druh dokumentu:	Working Paper
Popis:	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. Comment: 16 pages, 6 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1612.06482 Zobrazit plný text záznamu View this record from Arxiv