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Proof of a Conjecture of Goulden and Jackson

Published online by Cambridge University Press:  20 November 2018

Andrei Okounkov*
Affiliation:
Department of Mathematics, University of Chicago,5734 University Avenue, Chicago, IL, USA
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Abstract

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We prove an integration formula involving Jack polynomials conjectured by I. P. Goulden and D.M. Jackson in connection with enumeration of maps in surfaces.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1997

References

[C] Cherednik, I., Difference Macdonald-Mehta conjecture. Internat. Math. Res. Notices., to appear.Google Scholar
[D] Dunkl, C.F., Hankel transform associated to finite reflection groups. Contemp.Math. 138(1992), 123138.Google Scholar
[GHJ] Goulden, I.P., Harer, J.L., and Jackson, D.M., The virtual Euler characteristic for the moduli spaces of real and complex algebraic curves. Preprint September 1996.Google Scholar
[GJ] Goulden, I.P. and Jackson, D.M. Maps in locally orientable surfaces and integrals over real symmetric matrices. Canad. J. Math. (this issue).Google Scholar
[K] Kadell, K., An integral for the product of two Selberg-Jack symmetric polynomials. Compositio Math, (1) 87(1993), 543.Google Scholar
[M1] Macdonald, I.G., Some conjectures for root systems. SIAM J. Math. Anal., (6) 13(1982), 9881007.Google Scholar
[M2] Macdonald, I.G., Symmetric functions and Hall polynomials. Oxford Math. Monographs, Oxford University Press, New York, 1995.Google Scholar
[OO] Okounkov, A. and Olshanski, G., Shifted Jack polynomials, binomial formula, and applications. Math. Res. Letters, 4(1997), 6978.Google Scholar