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We establish formulae for the moments of the moments of the characteristicpolynomials of random orthogonal and symplectic matrices in terms of certainlattice point count problems. This allows us to establish asymptotic formulaewhen the matrix-size tends to infinity in terms of the volumes of certainregions involving continuous Gelfand-Tsetlin patterns with constraints. Theresults we find differ from those in the unitary case considered previously

On the moments of the moments of the characteristic polynomials of Haar distributed symplectic and orthogonal matrices