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arXiv · 2104.13512

Quadratic coefficients of Goulden-Rattan character polynomials

Mikołaj Marciniak
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Abstract

Goulden-Rattan polynomials give the exact value of the subdominant part of the normalized characters of the symmetric groups in terms of certain quantities ($C_i$) which describe the macroscopic shape of the Young diagram. The Goulden-Rattan positivity conjecture states that the coefficients of these polynomials are positive rational numbers with small denominators. We prove a special case of this conjecture for the coefficient of the quadratic term $C_2^2$ by applying certain bijections involving maps (i.e., graphs drawn on surfaces).

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Mikołaj Marciniak. 2022-05-31. Quadratic coefficients of Goulden-Rattan character polynomials. https://arxiv.org/abs/2104.13512

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