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An explicit form for Kerov's character polynomials
Author(s):
I.
P.
Goulden;
A.
Rattan
Journal:
Trans. Amer. Math. Soc.
359
(2007),
3669-3685.
MSC (2000):
Primary 05E10;
Secondary 05A15, 20C30
Posted:
February 23, 2007
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Abstract:
Kerov considered the normalized characters of irreducible representations of the symmetric group, evaluated on a cycle, as a polynomial in free cumulants. Biane has proved that this polynomial has integer coefficients, and made various conjectures. Recently, Sniady has proved Biane's conjectured explicit form for the first family of nontrivial terms in this polynomial. In this paper, we give an explicit expression for all terms in Kerov's character polynomials. Our method is through Lagrange inversion.
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Additional Information:
I.
P.
Goulden
Affiliation:
Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
Email:
ipgoulden@math.uwaterloo.ca
A.
Rattan
Affiliation:
Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
Address at time of publication:
Department of Applied Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Email:
arattan@math.mit.ca
DOI:
10.1090/S0002-9947-07-04311-5
PII:
S 0002-9947(07)04311-5
Received by editor(s):
April 20, 2005
Posted:
February 23, 2007
Copyright of article:
Copyright
2007,
American Mathematical Society
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