Asymptotics of multinomial sums and identities between multi-integrals
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We calculate the asymptotics of combinatorial sums ∑α f (α) (nα)3 where α = (αl, . . ., αh) with αi = αj. Here h is fixed and the αi's are natural numbers. This implies the asymptotics of the corresponding Sn-character degrees ∑λ f (λ)d3λ. For certain sequences of Sn characters which involve Young's rule, the latter asymptotics were obtained earlier  by a different method. Equating the two asymptotics, we obtain equations between multi-integrals which involve Gaussian measures. Special cases here give certain extensions of the Mehta integral , .
author list (cited authors)
Cohen, P. B., & Regev, A.