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Double Hurwitz numbers via the infinite wedge

Author: Paul Johnson
Journal: Trans. Amer. Math. Soc. 367 (2015), 6415-6440
MSC (2010): Primary 14N10
Published electronically: April 1, 2015
MathSciNet review: 3356942
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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.

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Additional Information

Paul Johnson
Affiliation: Department of Mathematics, Weber Building, Colorado State University, Fort Collins, Colorado 80523-1874
Address at time of publication: School of Mathematics and Statistics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH, United Kingdom

Received by editor(s): March 6, 2013
Received by editor(s) in revised form: July 9, 2013
Published electronically: April 1, 2015
Additional Notes: This research was supported in part by NSF grants DMS-0602191 and DMS-0902754.
Article copyright: © Copyright 2015 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.