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Gessel's famous Bessel determinant formula gives the generating function ofthe number of permutations without increasing subsequences of a given length.Ekhad and Zeilberger proposed the challenge of finding a suitablegeneralization for permutations of multisets in which all multiplicities areequal, that is, to count words of length $rn$ from an alphabet consisting of$n$ letters in which each letter appears exactly $r$ times and which have noincreasing subsequences of length $d$.  In this paper we present such a generating function expressible as a multipleintegral of the product of a Gessel-type Toeplitz determinant with theexponentiated cycle index polynomial of the symmetric group on $r$ elements.

On longest increasing subsequences in words in which all multiplicities are equal