Resumen de Upper bound on the characters of the symmetric groups for balanced Young diagrams and a generalized Frobenius formula

Amarpreet Rattan, Piotr Sniady

• We study asymptotics of an irreducible representation of the symmetric group Sn corresponding to a balanced Young diagram ? (a Young diagram with at most rows and columns for some fixed constant C) in the limit as n tends to infinity. We show that there exists a constant D (which depends only on C) with a property that where |p| denotes the length of a permutation (the minimal number of factors necessary to write p as a product of transpositions). Our main tool is an analogue of the Frobenius character formula which holds true not only for cycles but for arbitrary permutations.