dc.contributor.author |
Raichev, Alexander |
en |
dc.contributor.author |
Wilson, Mark |
en |
dc.date.accessioned |
2013-11-20T22:51:02Z |
en |
dc.date.issued |
2008 |
en |
dc.identifier.citation |
Electronic Journal of Combinatorics 15(1):17 pages Article number R89 2008 |
en |
dc.identifier.uri |
http://hdl.handle.net/2292/21134 |
en |
dc.description.abstract |
Let ∑β∈NdFβxβ be a multivariate power series. For example ∑Fβxβ could be a generating function for a combinatorial class. Assume that in a neighbourhood of the origin this series represents a nonentire function F=G/Hp where G and H are holomorphic and p is a positive integer. Given a direction α∈Nd+ for which the asymptotics are controlled by a smooth point of the singular variety H=0, we compute the asymptotics of Fnα as n→∞. We do this via multivariate singularity analysis and give an explicit uniform formula for the full asymptotic expansion. This improves on earlier work of R. Pemantle and the second author and allows for more accurate numerical approximation, as demonstrated by our our examples (on lattice paths, quantum random walks, and nonoverlapping patterns). |
en |
dc.relation.ispartofseries |
Electronic Journal of Combinatorics |
en |
dc.rights |
Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. Details obtained from http://www.combinatorics.org/ojs/index.php/eljc/about/submissions#copyrightNotice |
en |
dc.rights.uri |
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm |
en |
dc.title |
Asymptotics of Coefficients of Multivariate Generating Functions: Improvements for Smooth Points |
en |
dc.type |
Journal Article |
en |
pubs.issue |
1 |
en |
pubs.volume |
15 |
en |
pubs.author-url |
http://www.combinatorics.org/ojs/index.php/eljc/article/view/v15i1r89 |
en |
dc.rights.accessrights |
http://purl.org/eprint/accessRights/OpenAccess |
en |
pubs.subtype |
Article |
en |
pubs.elements-id |
78959 |
en |
pubs.org-id |
Science |
en |
pubs.org-id |
School of Computer Science |
en |
pubs.arxiv-id |
1009.5715 |
en |
dc.identifier.eissn |
1077-8926 |
en |
pubs.number |
R89 |
en |
pubs.record-created-at-source-date |
2010-09-01 |
en |