An explicit form for Kerov's character polynomials

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dc.creatorGoulden, I. P.
dc.creatorRattan, A.
dc.date2005-05-15
dc.date.accessioned2026-07-07T05:19:55Z
dc.date.available2026-07-07T05:19:55Z
dc.descriptionKerov 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.
dc.description17 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/math/0505317
dc.identifierhttp://arxiv.org/abs/math/0505317
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75201
dc.subjectCombinatorics
dc.subjectRepresentation Theory
dc.subject05E10 (Primary) 05A15, 20C30 (Secondary)
dc.titleAn explicit form for Kerov's character polynomials
dc.typetext

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