Johnson, P. (2015) Double Hurwitz numbers via the infinite wedge. Transactions of the American Mathematical Society , 367 (9). pp. 6415-6440. ISSN 0002-9947
Abstract
We derive an algorithm to produce explicit formulas for certain generating functions of double Hurwitz numbers. These formulas generalize a formula in the work of Goulden, Jackson, and Vakil for one part double Hurwitz numbers. Consequences include a new proof that double Hurwitz numbers are piecewise polynomial, an understanding of the chamber structure and wall crossing for these polynomials, and a proof of the Strong Piecewise Polynomiality Conjecture of their work.
The proof is an application of Okounkov's expression for double Hurwitz numbers in terms of operators on the infinite wedge. We begin with a introduction to the infinite wedge tailored to our use.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2015 American Mathematical Society. This is an author produced version of a paper subsequently published in Transactions of the American Mathematical Society. Uploaded in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 03 Feb 2016 16:05 |
Last Modified: | 09 Mar 2016 01:27 |
Published Version: | http://dx.doi.org/10.1090/tran/6238 |
Status: | Published |
Publisher: | American Mathematical Society |
Refereed: | Yes |
Identification Number: | 10.1090/tran/6238 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:94062 |