Asymptotics of multinomial sums and identities between multi-integrals Academic Article uri icon

abstract

  • 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 [1] 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 [5], [6].

author list (cited authors)

  • Cohen, P. B., & Regev, A.

citation count

  • 0

publication date

  • December 1999