Let Rn (α) be the n! × n! matrix whose matrix elements [Rn (α)]σρ, with σ and ρ in the symmetric group , are αℓ (σρ–1) with 0 < α < 1, where ℓ(π) denotes the number of cycles in π ∈ . We give the spectrum of Rn and show that the ratio of the largest eigenvalue λ0 to the second largest one (in absolute value) increases as a positive power of n as n → ∞.
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