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

• Autores: Amarpreet Rattan, Piotr Sniady
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 218, Nº 3, 2008, págs. 673-695
• Idioma: inglés
• DOI: 10.1016/j.aim.2008.01.008
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• Resumen

  • 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.