Title	Multivariate Algebraic Generating Functions: Asymptotics and Examples
Creator	Greenwood, Torin
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2017-09-19T16:30
Description	We find a formula for the asymptotics of the coefficients of a generating function of the form, $H(z_1, z_1, ..., z_d)^{-\beta}$, as the indices approach infinity in a fixed ratio. Then, we look at how this formula can be applied to generating functions that enumerate the possible structures into which RNA sequences can fold. This work relies on the techniques in multivariate analytic combinatorics developed by Pemantle and Wilson. We combine the multivariate Cauchy integral formula with explicit contour deformations to compute the asymptotic formula. A challenge of using the formula is correctly identifying the points which contribute to asymptotics.
Extent	27 minutes
Subject	Mathematics; Combinatorics; Sequences, series, summability; Discrete mathematics
Type	Moving Image
File Format	video/mp4
Language	eng
Notes	Author affiliation: Georgia Institute of Technology
Series	BIRS Workshop Lecture Videos (Banff, Alta)
Date Available	2018-03-31
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0364599
URI	http://hdl.handle.net/2429/65043
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Postdoctoral
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
Aggregated Source Repository	DSpace

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Multivariate Algebraic Generating Functions: Asymptotics and Examples Greenwood, Torin

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